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Full text of "Opticks: or, A treatise of the reflexions, refractions, inflexions and colours of light. Also two treatises of the species and magnitude of curvilinear figures"

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bPTICKS- 

O R , A 

TREATISE 

O F T H E 

REFLEXIONS, REFRACTIONS, 
INFLEXIONS and COLOURS 

OF 

L 1 Gr H T» 

ALSO 

Two TREATISES 

O F T H E 

SPECIES and MAGNITUDE 

O F 

Curvilinear Figures. 



LONDON^ p 

Printed for S.^m Smith, and Ben J, WaLf^r?; 

Printers to the Royal S ociety , at the Vr'mci's Arms in 
St. ?tiul\ Church-yard. MDCCIV* 4? ij / 



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ADVERTISEMENT. 



Art of the enfuing Difcourfe about Li^t wa^ written 
at the defire ofjome Gentlemen of the Royal Society, 

in the Tear i6'j^. and then fent to their Secretary y and 
read at their Meetings ^ and the reft was added about 
Twelve Tears after to complete the Theory ; except the 
Third Book J and the laji Propofition of the Second^ which 
were fine e put together out of f cotter ed Papers. To avoid 
being engaged in Difputes about thefe Matters^ I have 
hitherto delayed the Printings and fhould fliJl have dc" 
layed it^ had not the importunity of Friends prevailed upon 
me. If any other Papers writ on this Subject are got out 
of my Hands they are imperfect ^and were perhaps written 
before I had tried all the Experiments here fet down^ 
and fuUy fatisfied my f elf about the Laws of Refractions 
and Compqfition of Colours. I have here Publifhed what 
I think proper to come abroad^ wifhing that it may not be 
Tranflated into another Language 'without my Confent. 

The Crowns of Colours^ which fometimes appear about 
the Sun and Moon^ I have endeavoured to give an Ac-- 
count qf; but for want offufficient Obfervations leave that 
Matter to be further examined. The Subject- of the Third 
Book I have alfo left imperfect ^ not having tried all the 

Expe- 



iLxperiments which I intended when I was ahout theje 
Matters, nor repeated fome of thofe which^I did try^ until 
Ihadfatisfied my f elf ahutMJltheir CiriMmJiances. To 
communicate what. I -have tried^ and leave the resi to 
others for further Enquiry ^ ts all my Dejiga in puhlifhing 
tkefe Papers, 

In a Letter written to-MrJ-jdhnit'Lin the Tear i6j6, 
and puhhfhed hy Dr. Waliis^ / mentioned a Method hy 
wJjtch I had found fome- general Theorems ahout fquaring 
■Curvilmear .Figures j^^orcomp^ them with the Conic 
Sections J or other the JimpleB Figures with which they may 
I^e compared. And fome Tears ago I lent out a Manufcript 
containing fuchThcorems\ and having fine e met with fome 
Things copied out of it^ I have -m this: Occafion made it 
puhlickj prefixing to tt an Introdudlion and fuhjoyning a 
Scholium concerning that Method. And I have joined 
with it another fmall Traci concerning the Curvilinear 
Figures of the Second Kind^ which was alfo written 
many Tears ago^ and made Imown to fome Friends^ who 
have folictted the making it puUich 



I. 



CO 
The FIRST BOOK 

O F 

O P T I C K S 

PART I. 



MY Defign in this Book is not to explain the Pro- 
perties of Light by Hypothefes, but to propofc 
and prove them by Reafon and Experiments : 
In order to which , I fliall premife the following Defini- 
tions and Axioms. 

DEFINITIONS. 

D E F I N. L 

T lihe ^ys of Light I underfland its leajl Tarts , and thofe 

as weliSucceJ/l'Ve in the fame Liries as Contemporary in fe^ 

l^eral Lines, For it is manifeft that Light confifts of parts 
both Succeflive and Contemporary 3 becaufe in the fame 
place you may flop that which comes one moment, and 
let pafs that which comes prefently after3 and in the fame 
time you may flop it in any one place, and let it pafs in 
any other. For that part of Light which is ftopt cannot 
be the fame with that which is let pafs. The leaft Light 
or part of Light , which may be ftopt alone without the 
reft of the Light, or propagated alone, or do or fufter any 

A thing 




thing alone, which the reft of thf Light doth not or fut 
ers not, I all a Ray of jLi^. 

D E F I N. II. 

^frangtbilky of the ^ys of Light^ is their Difpojition to he 
refrahed or turned out of their Way in pajjing out of one tranf^ 
parent ^ody or Medium into another. And a greater or lefs (?^e- 
frangihility of^ys^ is their Difpojition to be turmd more or lefs 
out of their Way in like Incidences on the fame Medium. Mathe- 
maticians ufually confider the Rays of Light to be Lines 
Teaching from the luminous Body to the body illumina- 
ted, and the refradlion of thofe Rays to be the bending 
or breaking of thofe Lines in their pafling out of one Me- 
dium into another. And thus may Rays and Refradions 
be confidered, if Light be propagated in an inftant. But 
by an Argument taken from the Equations of the times 
of the Eclipfes o? Jupiter's Satellites it feems that Light is 
propagated in time, fpending in its paffage from the Sun 
to us about Seven Minutes of time : And therefore I have 
chofen to define Rays and Refradions in fuch general 
terms as may agree to Light in both cafes. 

DBF I N. IIL 

'^flexibility of ^ys^ is their Difpojition to be turned baci ^^^^ 
■the fame Medium from any other Medium upon whofe Surface they 
fall. And ^ys are 7?iore or le[^ reflexible , which are returned 
hack ^ore oiSefs eaftly. As if Light pafs out of Glafs into 
Air and by being incHned more and more to the com- 
mon Surface of the Glafs and Air, begins at length to be 
totally refleded by that Surface 3 thofe forts of Rays which, 
at like Incidences are refleded moft copioufly , or by in- 
clining the Rays begin fooneft to be totally refleded, are 
moft reflexible. 53 E- 



t 33 

DEFiN. nr, 

T%e Angle of Incidence^ is that Angle which the Line defcribei 
hy the incident ^y contains with the Perpendicular to the reflc" 
Bing or refraBing Surface at the ^oint of Incideme, 

DEFIN. V. 

The Angle of ^flexion or ^fraBion^ is the Angle which the 
Line defcrihed hy the refleBed or refraBed ^y containeth with 
the Perpendicular to the refleBing or refraBing Surface at the 
Point of Incidence. 

DEFIN. VI. 

T%e Sines of Incidence^ ^flexion^ and ^fraBion^ are the 
Sines of the Angles of Incidence^ ^flexion^ and ^efraBion, 

DEFIN. VII. 

The Light whofe (^ys are all alike ^frangihle^ I call Simm 
pky Homogoieal and Similar-^ and that whofe ^ys are feme 
more ^frangible than others^ I call Compound^ Heteroo-eneal and 
DiJJlmilar. The former Light I call Homogeneal , not 
becaiife I would affirm it fo in all relped:s 3 but becaufe 
the Rays which agree in Refrangibility , agree at leaft ia 
all thofe their other Properties. Which I confider in the 
following Difcourfe. 

DEFIN. VIII. 

The Colours of Homogeneal Lights , I call Primary^ HomO" 
geneal and Si?nple 5 and thofe of Heterogeneal Lights^ Heteroge" 
neal and Compound, For thefe are always compounded of 
the colours of Homogeneal Lights 3 as will appear in the 
following Difcourfe. A 2 AX I- 



c 4 J : : : 

A X I M S. 

A X, L 

TH E Angles of Incidence^ (^flexion, and ^fraBioUy lye 
in one and the fame ^latie. 

A X. IL 

The Angle of ^flexion is equal to the Angle of Incidence. 

A X. III. 

If the refraSied ^y he returned direBly hack^ to the ^oint 
of Incidence , it fhall be ref rafted into the Line before defcri' 
M hy the incident <S^y. 

AX. IV. 

^fraBion out of the rarer Medium into the denfer , is made: 
towards the perpendicular 3 that is^ fo that the Angle of (^^fra-, 
Bion he kf? than the Angle of Incidence. 

A X. V. 

T^he Sine of Incidence ^ is either accurately or Very nearly in a 
given <^tio to the Sine of^efraBion.. 

Whence if that Proportion be known in any one Ihcli'^ 
nation of the incident Ray, 'tis known in all the Inclina- 
tions and thereby the Refrad:ion in all cafes of Incidence 
on the fame refrading Body may he determined. Thus 
if the Refradion be made out of Air into Water, the Sine 
of Incidence of the red Light is to the Sine of its Refra- 
dicn as 4 to ?» If out of Air into Glafs, the Sines are. 



en 

as 17 to 1 1. In Light of other Colours the Sines have 
other Proportions : but the difference is fo little that it 
need feldom be confidered. 

Suppofe therefore, that R S reprefents the Surface of F/?. s 
ftagnating Water, and^C is the point of Incidence in. 
which any Ray coming in the Air from A in the Line 
A C is refleded or refraded, and I would know whether 
this Ray fliall go after Reflexion or Refradion : I eredt 
upon the Surface of the Water from the point of Inci* 
dence the Perpendicular C P and produce it downwards, 
to Q, and conclude by the firfl; Axiom, that the Ray af- 
ter Reflexion and Refradion, fliall be found fomewhere in. 
the Plane of the Angle of Incidence A C P produced. I 
let fall therefore upon the Perpendicular CP the Sine of 
Incidence A D, and if the reflected Ray be defired , I pro- 
duce A D to B fo that D B be equal to A D, and draw: 
C B. For this Line C B fliall be the reflected Ray 5 the 
Angle of Reflexion B C P and its Sine B D being equal 
to the Angle and Sine of Incidence, as they ought to be 
by the fecond Axiom. But if the refradled Ray be de^ 
fired, I produce A D to H, fo that D H may be to A D 
as the Sine of Refraction to the Sine of Incidence that is 
as 3 to 4 5 and about the Center C and in the Plane A C P 
with the Radius C A defcribing a Circle A B E I draw 
Parallel to the Perpendicular C P Q, the Line H E cutting 
the circumference in E, and joyning C E, this Line CE 
fliall be the Line of the refraded Ray. For if E F be let 
fall perpendicularly on the Line P Q , this Line E F fliall 
be the Sine of Refradion of the Ray C E, the Angle of 
Refradion being E C Q.3 and this Sine E F is equal ta 
D H, and confequently in Proportion to the Sine of Inci-^- 
dence AD as 3 to 4. 



, ) 



In like maft^ner, if there be a Prifm of Glafs (that is a 
Glafs bounded with two Equal and Parallel Triangular 
ends, and three plane and well poliflied Sides, which meet 
in three Parallel Lines running from the three Angles of 
one end to the three Angles of the other end) and if the 
Refraction of the Light in paffing crofs this Prifm be defi- 
red : Let ACB reprefent a Plane cutting this Prifm tranf- 
verily to its three Parallel lines or edges there vvhere the 
Light paffeth through it, and let BE be the Ray inci- 
dent upon the firft fide of the Prifm A C where the Light 
goes into the Glafs 3 And by putting the Proportion of 
the Sine of Incidence to the Sine of Refraction as 1 7 to 
1 1 find E F the firft refraCled Ray. Then taking this Ray 
for the Incident Ray upon the fecond fide of the Glafs B C 
where the Light goes out, find the next refracted Ray F G 
by putting the Proportion of the Sine of Incidence to the 
Sine of RefraClion as 11 to 17. For if the Sine of Inci- 
dence out of Air into Glafs be to the Sine of Refra6tion 
as 1 7 to II, the Sine of Incidence out of Glafs into Air 
muft on the contrary be to the Sine of RefraCtion as 1 1 
to 17, by the third Axiom. 

Much after the fame manner , if A C B D reprefent a 
Glafs fpherically Convex on both fides (ufually called a 
Leyis^ fuch as is a Burning- glafs, or Spectacle-glafs, or an 
Objed' glafs of a Telefcope) and it be required to know 
how Light falling upon it from any lucid point Q. fliall 
be refracted, let Q.M reprefent a Ray falling upon any 
point M of its firft fpherical Surface ACB, and by erecting 
a Perpendicular to the Glafs at the point M , find the firft 
refracted Ray M N by the Proportion of the Sines 1 7 
to 1 1 . Let that Ray in going out of the Glafs be inci- 
dent upon N, and then find the fecond refracted Ray N ^ 
by the Proportion of the Sines 11 to 17. And after the 

fame 



[7] 

fame ma^nner may the Refiadion he found when die 
Lens is Convex on one fide and Plane or Concave on 
the other, or Concave on both Sides. 

AX. VI. 

Hoinogenecd ^ys which flow from feVerdl joints of any Oh^ 
jeEi^ md fall almoft Perpendicularly on any refleHing or refra^ 
Bing <Plane or Spherical Surface y fhall afterwards diverge from 
fo niafiy other Toints, or he Parallel to Jo many other Lines ^ or 
C07iVerge to fo many other Toints, either accurately or without any 
fenfihle Error. Jjid the fame thing will happen^ if the ^ys he 
reflected or refraBed fuccejjlyely hy two or three or more ^lane 
or jj^herical Surfaces, 

The Point from which Rays diverge or to which they 
converge may be called their Focus. And the Focus of 
the incident Rays being given, that of the refledled or re« 
firadled ones may be found by finding the Refradlionof 
any two Rays, as above 5 or more readily thus, ^ 

Caf 1. Let ACBbe a reflecting or refracting Plane, F^. 4^ 
and Q, the Focus of the incident Rays, and Q^ C a per- 
pendicular to that Plane. And if this perpendicular be 
produced to ^, fo that q C be equal to Q.C, the point q^ 
fhall be the Focus of the reflected Rays. Or if ^ C be 
taken on the fame fide of the Plane with Q_C and in Pro- 
portion to (iC as the Sine of Incidence to the Sine of 
Refiradion, the point q fhall be the Focus of the refrac- 
ted Rays. 

Caf. 2. Let A C B be the reflecting Surface of any Fig^ 5. i 

Sphere whofe Center is E. Bifect any Radius thereof (fup- C\/^fl/^&^ \ 
pofe E C) in T, and if in that Radius on the fame fide the p^<clU^^ctir.f>. ^ 
point T you take the Points Q. and ^, fo that T Q, T E, ^'"^1 

and T^ be continual Proportionals, and the point Qbe 

the. 



C 8 ] 

the Focus of the incident Rays , the point q ihall be the 
Focus of the refledled ones. 
SF^, 6. Caf. ^ . Let A C B be the refracting Surface of any 

^^-(i)^//: tK^/' Sphere whofe Center is E. In any Radius thereof EC 

g//c^l4. ^- n-a^^^ produced both ways take E T and C t lMM^ in fuch 
Proportion ^to"^ that Radius as the lefler of the Sines of 
Incidence and Refraction hath to the difference of thofe 
Sines. And then if in the fame Line you find any two 
Points Q. and q , fo that T Q. be to E T as E t to f ^, 
taking t q the contrary way from t which T Q. lieth from 
T, and if the Point Q.be the Focus of any incident Rays, 
the Point q fhall be the Focus of the refradled ones. 

And "by the fame means the Focus of the Rays after 
two or more Reflexions or RefiraCtions may be found. 
jF^'7' €af, /^, Let A C B D be any refracting Lens , fpheri- 

Q^^-W?/i7at^>yfeally Convex or Concaye or Plane on either lide, and let 
f, ^^. C D be its Axis (that is the Line which cuts boih its Sur- 

faces perpendicularly, and paffes through the Centers of 
the Spheres,) and in this Axis let F and/be the Foci of the 
refracted Rays found as above , when the incident Rays 
on both fides the Lens are Parallel to the fame Axis 3 and 
upon the Diameter F/ bifected in E, defcribe a Circle. 
Suppofe now that any Point Q be the Focus of any inci- 
dent Rays. Draw Q.E cutting the faid Circle in T and f, 
and therein take t q in fuch Proportion to ^ E as f E or T E 
hath to T Q. Let t q lye the contrary way from t which 
T Q, doth from T, and q fhall be the Focus of the refrac- 
ted Rays without any feniible Error , provided the Point 
Q be not fo remote from the Axis, nor the Lens fo broad 
as to make any of the Rays fall too obliquely on the 
refracting Surfaces. 

And by the like Operations may the reflecting or re- 
fracting Surfaces be found when the two Foci are given, 

\ and 



[p] 

and thereby a Lens be formed, which fliall make the Rays 
flow towards or from what place you pleafe. 

So then the meaning of this Axiom is , that if Rays 
fall upon any Plane or Spherical Surface or Lens, and 
before their Incidence flow from or towards any Point Ql, 
they fhall after Reflexion or Refraction flow from or to- 
wards the Point q found by the foregoing Rules. And if 
the incident Rays flow from or towards feveral points Q., 
the reflected or refracted Rays fhall flow from or towards 
fo many other Points q found by the fame Rules. Whe- 
ther the reflected and refracted Rays flow from or towards 
the Point q is eafily known by the fituation of that Point. 
For if that Point be on the fame fide of the reflecting or 
refracting Surface or Lens with the Point Q, and the in- 
cident Rays flow from the Point Q, , the refle(5led flow to- 
wards the Point q and the refracted from it 5 and if the 
incident Rays flow towards Q_, the reflected flow from q, 
and the refracted towards it. And the contrary happens 
when q is on the other fide of that Surface. 

AX. VII. 

Wherever the ^ys which come from all the joints of any Ob" 
jeB meet again info many Joints after they ha'Ve been tnade to 
converge hy ^flexion or ^fraBion^ there they ivill make a Tic" 
ture of the Object upon any ivhite !Body on which they fall. 

So if PR reprefent any Object without Doors, and AB Fig, 
be a Lens placed at a hole in the Window-fliut of a dark 
Chamber, whereby the Rays that come from any Point Q. 
of that Object are made to converge and meet again in 
the Point q 5 and if a Sheet of white Paper be held at q 
for the Light there to fall upon it : the Picture of that 
Object PR will appear upon the Paper in its proper Shape 

B and 



[lOj 

and Colours. For as the Light which comes from the 
Point Qgoes to the Point qy fo the Light which comes 
from other Points P and R of the Object, will go to fo 
many other correlpondent Points p and r (as is ma:tiife{fc 
by the fixth Axiom 3 ) fo that every Point of the Object 
fliall illuminate a correfpondent Point of the Picture, and 
thereby make a Picture like the Object in Shape and Co- 
lour, this only excepted that the Picture fliall be inverted, 
•And this is the reafon of that Vulgar Experiment of caft- 
ingthe Species of Objects from abroad upon a Wall or 
Sheet of white Paper in a dark Room. 

In like manner when a Man views any Object P Q.R5 
the Light which comes from the feveral Points olthe Ob- 
ject is fo refracted by the tranfparent skins and humours 
of the Eye, (that is by the outward coat EFG called the 
Tunica Cornea, and by the cryftalline humour AB which is 
beyond the Pupil m k,) as to converge and meet again at 
fo many Points in the bottom of the Eye, and there to paint 
the Picture of the Object upon that skin (called the 7«- 
nica ^tina) with which the bottom of the Eye is covered. 
For Anatomifts when they have taken off from the bot- 
tom of the Eye that outward and moft thick Coat called 
the Dura Mater, can then fee through the thinner Coats 
the Pictures of Objects lively painted thereon. And thefe 
Pictures propagated by Motion along the Fibres of the Op- 
tick Nerves into the Brain, are the caufe of Vifion. For 
accordingly as thefe Pictures are perfect or imperfect, the 
Object is feen perfectly or imperfectly. If the Eye be tin- 
ged with any colour fas in the Difeafe of the Jaundife) fo 
as to tinge the Pictures in the bottom of the Eye with that 
Co4our, then all Objects appear tinged with the fame Co- 
lour. If the humours of the Eye by old Age decay, fo 
as by flirinking to make the Cornea and Coat of the Cry-' 

Jlalline 



In] 

fliiSkehumaur. grow &2cmxth^nh^ the Light will not be 
refracted .enough, aad for want of a fufficient Reftadion 
vvijlnot cQavergejto the bottom of the Eye but tofome 
place beyond it , and by confequence paint in the bottom 
of the Eye aconfufedPidure^and according to the indiftind- 
jiefs of this Pidlure the Gbje(5l will appear confufed. This 
is the reafon of the decay of Sight in old Men, and fliews 
why their Sight is mended by Spe(5tacles. For thofe Con- 
vex- glafles fupply the defe(5l ofplumpnefs in the Eye, and 
by encreafingtheRefradlion make theRays converge fooner 
:fo^s to convene diftindtly at the bottom of the Eye if the 
Gkfs have a ducidegree of convexity. And the contrary 
happens in fliort-fighted Men whofe Eyes are too plump. 
For the Refraction being now too great, the Rays converge 
and convene in the Eyes before they come at the bottom 3 
and therefore the Pidure made in the bottom and theVifion 
caufed thereby will not be diftinft, unlefs the Objed be 
brought fo near the Eye as that the place where the con- 
verging Rays convene may be removed to the bottom, or 
that the plumpnefs of the Eye be taken off and the Refra- 
dlions diminifhed by a Concave-glafs of a due degree of 
Concavity, or laftly that by Age the Eye grow flatter till it 
come to a due Figure : For (hort-fighted Men fee remote 
Objeds beft in Old Age, and therefore they are accounted 
to have the mofl lafting Eyes. 

A X. VIII. 

Jn ObjeFt feen hy ^flexion or ^efraEiion^ appears in that place 
from whence the ^ys after their laft ^flexion or ^fraSiion di' 
"Verge in falling on the SpeBators Eye. 

If the Objed A be feen by Reflexion of a Looking- Fig* p» 
glafs m Hy it fliall appear, not in it's proper place A, but 

B 2 behind 



[12] 

behind the Glafs at a^ from whence any Rays AB, AC, 
AD, which flow from one and the fame Point of the Ol> 
je<^5 do after their Reflexion made in the Points B,C, D, 
diverge in going from the Glafs to E, F, G, where they 
are incident on the Spectator's Eyes. For thefe Rays do 
make the fame Picture in the bottom of the Eyes as if 
they had come from the Object really placed at a without 
the interpofition ©f the Looking- glafs 5 and all Vifion is 
made according to the place and fhape of that Picture. 

'k. 2. In like manner the Object D feen through a Prifm ap- 
pears not in its proper place D, but is thence tranflated to 
lome other place d fituated in the laft refracted Ray F G 
drawn backward from F to d. 

fig. \o> And fo the Object Q_ feen through the Lens A B, appears 
at the place q from whence the Rays diverge in paffing 
from the Lens to the Eye. Now it is to be noted, that the 
Image of the Object at ^ is fo much bigger or leffer than 
the Object it felf at Q., as the diftanee of the Image at 
q from the Lens AB is bigger or lefs than the diftanee of 
the Object at Q. from the fame Lens; And if the Object 
be feen through two or more fuch Convex or Concave- 
glafles, every Glafs fhall make a new Image, and the Ob- 
jedfhal! appear in the place and of the bignefs of the laft 
Image. Which confideration unfolds the Theory of Mi- 
crofcopes and Telefcopes. For that Theory confifts in al- 
moft nothing elfe than the defcribing fuch Glafles as fliall 
make the laft Image of any Objed" as diftind and large: 
and luminous as it can conveniently be made. 

I have now given in Axioms and their Explications the 
ftimm of what hath hitherto been treated of in Opticks» 
For, what hath been generally agreed on I content my 
felf to afllime under the notion of Principles, in order to 
what I have further to write. And this may fuffice for an 

Intro« 



[13 1 

TntroduAion to Readers of quick Wit and good Under^ 
ftanding not yet verfed in Opticks : Although thofe who 
are already acquainted with this Science , and have 
handled Glafles, will more readily apprehend what fol- 
loweth. 



PROPOSITIONS. 



L 



^%^0T, I. Theor. I. 

I G H T S which differ in Colour, differ alfo in De- 
grees of Refrangibility, 

The Proof hy Experiments: 



Exper. \ . I took a black oblong fliff Paper terminated 
by Parallel Sides, and with a Perpendicular right Line 
drawn crofs from one Side to the other , diflinguiflhed it 
into two equal Parts. One of thefe Parts I painted with 
a red Colour and the other with a blew. The Paper was 
very black, and the Colours intenfe and thickly laid on, 
that the Phaenomenon might be more confpicuous. This 
Paper I viewed through a Prifm offolid Glafs, whofe two 
Sides through which the Light pafled to the Eye were 
plane and well poliflhed, and contained an Angle of about 
Sixty Degrees : which Angle I call the refrading Angle of 
the Prifm. And whilft I viewed it, I held it before a c j^"^*"^ 
Window in fuch manner that the Sides of the Paper were 
parallel to the Prifm, and both thofe Sides and the Prifm 
parallel to the Horizon, and the crofs Line perpendicular 
to it 3 and that. the Light which fell from the- Window 



, 



-;pf on the Paper made an 4l^le with the Paper^ :equal tp 
that Angle which was made with the fame Paper by the 
,Light renefted from it to the Eye. Beyond the Prifm was 
-the Wall of the Chamber under the Window covered, over 
with black Cloth, and the Cloth was involved in Daifk- 
nefs that no Light might be refleded from thence, which 
in paffing by the edges of the Paper to the Eye , might 
mipgle it felf with the Light of the Paper aad obfcure the 
Phsenomenon thereof Thefc things being thus ordered, 
I found that if the refradling Angle of the Prifm be turned 
upwards, fo that the Paper may feem to be lifted upwards 
by the Refradion, its blew half will be lifted higher by 
#he fRefra<5lion than its red half But if the refracting 
Angle of the Prifm be turned downward, fo that the Pa- 
per may feem to be carried lower by the Refrad:ion, its 
tlew half will be carried fomething lower thereby than 
its red half Wherefore in both cafes the Light which 
comes from the blew half of the Paper through the Prifm 
^to the Eye, does in like Circumftances fuffer a greater R^- 
fradlion than the Light which comes from the red half, 
and by confequence is more refrangible. 
Fig. 1 1. Ilkflratioru In the Eleventh Figure, M N reprefents the 
Window,and D E the Paper terminated with parallel Sides 
D J and HE, and by the tranfverfe Line F G diflinguiflhed 
into two halfs, the one D G of an intenfely blew Colorur, 
the other FEof an intenfely red. AndBACc^^ repr,e- 
fents the Prifm whofe refracting Planes K^b a and KQca 
meet in the edge of the refracting Angle A a. This edge 
Act being upw^ard, is parallel Ippth jto the Horizon and -to 
the parallel edges or tnePapd' DJ and H E.a And a^re- 
prefents the Image of the Paper feen by RefraCtion up- 
wards in fuch manner that the blew half D G is carried 
higher to dg than the red half F E is to /e, and therefore 

fufFers 



'<i7ij f*r,/c 



fuffers^ X gfcatet Refra€Bon. If: the edge of the refrafting 
Angle be turned downward, the Image of the Paper will 
be rcfrad:ed downward fuppofe to ^6, and the blew half 
will be refrad^ed lower to ^ y- than the red half is to ?>f. 

Exper. 1. About the aforefaid Paper, whofe two halfe 
were painted over with red and blew/, and which was ftiff 
hke thin Paftboard, I lapped feveral times a flender thred 
of very black Silk, in fuch manner that the feveral parts 
of the thred might appear upon the Colours like fo many 
black Lines drawn over them , or like long and flender 
dark Shadows cafl: upon them. I might have drawn black 
Lines with a Pen, but the threds we^ fmalkr and better 

►er thus coloured aaadiaea I let ; 



defined. This Paper thus coloured arffiaeS I fet againft 
a Wall perpendicularly to the Horizon, fo that one of the 
Colours might fliand to the right hand and the other to 
the left. Clofe before the Paper at the confine of the Co- 
lours below I placed a Candle to illuminate the Paper 
ftrongly : For the Experiment was tried in the Night. 
The flame of the Candle reached up to the lower edge of 
the Paper, or a very little higher. Then at the difl:ance of 
Silc Feet and one or two Inches from the Paper upon the 
Floor I ere^led a glafs Lens four Inches and a quarter 
broad, which might coUedl the Rays coming from the 
feveral Points of the Paper, and make them converge to- 
wards fo many other Points at the fame difl:ance of fix 
Feet and one or two Inches on the other fide of the Lens^ 
and fo form the Image of the coloured Paper upon a white 
Paper placed there 5 after the fame manner that a Lens at 
a hole in a Window cafl:s the Images of Objeds abroad 
upon a Sheet of white Paper in a dark Room. The afore- 
faid white Paper, ereded perpendicular to the Horizon 
and to the Rays which fell upon it fi'om the Lens, I moved 
fometimes towards the Lens, fometimes firom it, to finct 

the 



12. 



tlie places where the Images of the tlew and red parts of 
the coloured Paper appeared moll: diftind. Thofe places 
I eafily knew by the Images of the black Lines which I 
had made by winding the Silk about the Paper. For the 
Images of thofe fine and flender Lines (which by reafon of 
their blacknefs were like Shadows on the Colours) were 
Gonfiifed and fcarce vifible, unlefs when the Colours on ei- 
ther fide of each Line were terminated moft diftindlly. 
Noting therefore, as diligently as I could, the places where 
the Images of the red and blew halfs of the coloured Pa- 
per appeared moft diftin6l , I found that where the red 
half of the Paper appeared diftinifl, the blew half appeared 
eonfufed, fo that the black Lines drawn upon it could 
fcarce be feen 3 and on the contrary where the blew half 
appeared moft diftincS^ the red half appeared confufed, fo 
that the black Lines upon it were fcarce vifible. And be- 
tween the two places where thefe Images appeared diftinfl 
there was the diftance of an Inch and a half : the diftance 
of the white Paper from the Lens, when the Image of the 
red half of the coloured Paper appeared moft diftin(5t, be- 
ing greater by an Inch and an half than the diftance of the 
fame white Paper from the Lens when the Image of the 
blew half appeared moft diftin(5l. In like Incidences there- 
fore of the blew and red upon the Lens, the blew was re- 
fradted more by the Lens than the red^ fo as to converge 
fooner by an Inch and an half, and therefore is more refran- 
gible. 

Illuftratioru In the Twelfth Figure, D E fignifies the co- 
loured Paper, D G the blew half, F E the red half, M N 
the Lens, H J the white Paper in that place where the red 
half with its black Lines appeared diftindl, and hi the fame 
Paper in that place where the blew half appeared diftindl. 
The place hi was nearer to the Lens M N than the place 
H J by an Inch and an half. Scholium. 



[17] 

Scholium, The fame things fucceed notwithftanding that 
fome of the Circumftances be varied : as in the firft Ex- 
periment when the Prifm and Paper are any ways inclined 
to the Horizon , and in both when coloured Lines are 
drawn upon very black Paper. But in the Defcription of 
thefe Experiments , I have fet down fuch Circumftances 
by which either the Phsenomenon might be rendred more 
conlpicuous, or a Novice might more eafily try them, or 
by which I did try them only. The fame thing I have 
often done in the following Experiments : Concerning all 
which this one Admonition may fuffice. Now from thefe 
Experiments it follows not that all the Light of the blew 
is more Refrangible than all the Light of the red 5 For 
both Lights are mixed of Rays differently Refrangible, 
So that in the red there are fome Rays not lefs Refrangible 
than thofe of the blew , and in the blew there are fome 
Rays not more Refrangible than thofe of the red 5 But 
thefe Rays in Proportion to the whole Light are but fcWy 
and ferve to diminifh the Event of the Experiment , but 
are not able to deflroy it. For if the red and blew Co- 
lours were more dilute and weak, the diftance of the Ima- 
ges would be lefs than an Inch and an half 5 and if they 
were more intenfe and full, that diftance would be greater, 
as will appear hereafter. Thefe Experiments may fuffice 
for the Colours of Natural Bodies. For in the Colours 
made by the Refraction of Prifms this Propofition will 
appear by the Experiments which are now to follow in the 
next Propofition. 



^(^Of. 



[i8] 
P ROF. II. Theor. 11. 

The Light of the Sun confijls of ^ays differently (^frangible. 

The Proof by Experiments. 

Exper. 3. XN a Ycry dark Chamber at a round hole about 
^ one third part of an Inch broad made in the 
Shut of a Windovv/ I placed a Glafs Prifm, whereby the 
beam of the Sun's Light which came in at that hole might 
be refrad:ed upwards tovv^ard the oppofite Wall of the 
Chamber , and there form a coloured Image of the 
Sun. The Axis of the Prifm (that is the Line pafling 
through the middle of the Prifm from one end of it to 
the o:her end Parallel to the edge of the Refracflino; Angle) 
was in this and the following Experiments perpendicular 
to the incident Rays. About this Axis I turned tbe Prifm 
flowly , and faw the refradied Light on the Wall or cO" 
loured Image of the Sun firft to defcend and then to af^ 
etnd. Between the Defcent and Afcent when the Image 
feemed Stationary , I ftopt the Prifm, and fixt it in that 
Pofttire, that it (hould be moved no more. For in that 
pofture the Refractions of the Light at the two fides of 
the Refrading Angle, that is at the entrance of the Rays 
into the Prifm and at their going out of it, were equal to 
one another. So alfo in other Experiments as often as I 
would have the Refradlions on both fides the Prifm to be 
equal to one another, I noted the place where the Image 
of the Sun formed by the refracted Light fl;ood ftill be- 
tween its two contrary Motions, in the common Period 
' of its progrefs and egrefs 3 and when the Image fell upon 
tJiat fplace, I made faft the Prifm. A_nd in this pofture, as 

the 



[19] 

die moft convenient,it is to be underftood that all the Prifms 
are placed in the following Experiments, unlefs where fome 
other pofture is defcribed. The Prifm therefore being pla- 
ced in this pofture, I let the refraded Light fall perpendi- 
cularly upon a Sheet of white Paper at the oppofite Wall 
of the Chamber, and obfervcd the Figure and Dimeniions 
of the Solar Image formed on the Paper by that Light. 
This Image was Oblong and not Oval, but terminated 
with two Recftilinear and Parallel Sides , and two Semi- 
circular Ends. On its Sides it was bounded pretty diftindly, 
but on its Ends very confufedly and indiftin6lly, the Light 
there decaying and vanifliing by degrees. The breadth of 
this Image anfwered to the Sun s Diameter, and was about 
two Inches and the eighth part of an Inch , including the 
Penumbra. For the Image was eighteen Feet and an half 
diftant from the Prifm, and at this diftance that breadth if 
diminiflied by the Diameter of the hole in theWindow-flhut, 
that is by a quarter of an Inch, fubtended an Angle at the 
Prifm or about half a Degree, which is the Suns apparent 
Diameter. But the length of the Image was about ten Inches 
and a quarter, and the length of the Recftilinear Sides about 
eight Inches 5 And the refradring Angle of the Prifm where- 
by fo great a length was made, was 64. degr. With a kfs 
Angle the length of the Image was lefs , the breadth re-* 
maining the fame. If the Prifm was turned about its Axis 
that way which made the Rays emerge more obliquely out 
of the fecond refradinp; Surface of the Prifm, the Imao^e foon 
became an Inch or two longer, or more 5 and if the Prifm 
was turned about the contrary way, fo as to make the Rays 
fall more obliquely on the firft refrading Surface, the Image 
foon became an Inch or two fliorter. And therefore in try- 
ing this Experiment, I was as curious as I could be in pla- 
cing the Prifm by the above-mentionsd Rule exadly in 

C 2 fuch 



[20] 

filch a pofture that the Refradions of the Rays at their emer- 
gence out of the Prifm might be equal to that at their inci- 
dence on it. This Prifm had fome Veins running along 
within the Glafs from one end to the other , which feat- 
tered fome of th€ Sun's Light irregularly,, but had no fen- 
fible efFe6l in encreafing the length of the coloured Spec- 
trum. For I tried the fame Experiment with other Prifms 
with the fame Succefs. And particularly with a Prifm 
which feemed free from fuch Veins, and whofe refracting 
Angle was 61^ Degrees, I found the length of the Image 92 

01^ 10 Inches at the diftance of i 8- Feet from the Prifm, 
the breadth of the hole in the Window-fhut being i of an 

Inch as before. And becaufe it is eafie to commit a mi- 
ftake in placing the Prifm in its due pofture, I repeated 
the Experiment four or five times, and always found the 
length of the Image that which is fet down above. With 
another Prifm of clearer Glafs and better PoUifh, which 
feemed free from Veins and whofe refracting Angle was 
63 - Degrees, the length of this Image at the &me diftance 

of 1 8 { Feet was alfo about 1 o Inches, or 10^. Beyond 

thefe Meafures for about • or - of an Inch at either end of 

4 3 

the Spedtrum the Light of the Clouds feemed to be a little 
tin-ged with red and violet, but fo very faintly that I fufpe- 
Cted that tinCture might either wholly or in great meafure 
arife from fome Rays of the SpeCtrum fcattered irre- 
gularly by fome inequalities in the Subftance and Polifh 
of the Glafs , and therefore I did not include it in thefe 
Meafures. Now the different Magnitude of the hole in 
theWindow-fhut, and different thicknefs of the Prifm where 
the Rays paffed through it, and different inclinations of the 
Prifm to the Horizon, made no fenfible changes in the 
length of the Image. Neither did the different matter of 

the 



[ 21 ] 

the Prifms make any : for in a Veflel made of poliflied 
Plates of Glafs cemented together in the fliape of a Prifm? 
and filled with Water, there is the like Succefs of the Ex- 
periment according to the quantity of the Refrad:ion. It 
is further to be obferved, that the Rays went on in right 
Lines from the Prifm to the Image, and therefore at their 
very going out of the Prifm had all that Inclination to 
one another from which the length of the Image pro- 
ceeded, that is the Inclination of more than two Degrees 
and an half And yet according to the Laws of Opticks 
vulgarly received, they could not poffibly be fo much in* 
clined to one another. For let EG reprefent the Window- f/p-. j:9; 
fhut, F the hole made therein through which a beam of the 
Sun's Light was tranfmitted into the darkned Chamber, and 
A B C a Triangular Imaginary Plane whereby the Prifm is 
feigned to be cut tranfverfly through the middle of the 
Light. Or if you pleafe, let A B G reprefent the Prifm it 
felf, looking direcftly towards the Spe^fiator s Eye with its 
nearer end : And let X Y be the Sun, M N the Paper upon 
which the Solar Image or Spectrum is caft, and P T the 
Image it felf whofe fides towards V and W are Redili- 
near and Parallel, and ends towards P and T Semicir-- 
Gular. Y K HP and X L J T are -the two Rays, the firft 
of which comes firom the lower part of the Sun to the> 
higher part of the Image, and is refracted in the Prifm at 
K and H, and the latter comes from the higher part of 
the Sun to the lower part of the Image, and is refracted 
at L and J. Since the Refradions on both fides the Prifm 
are equal to one another, that is the Refradion at K equal 
to the Refradion at J, and the Refradion at L. equal to 
the Refradion at H, fo that the Refi:adions of the inci- 
dent Rays at K and L taken together are equal to the 
Refractions of the emergent Rays at H and J tai:ea toge^ 

ther ; 



4 



[22] 

Aer : it follows by adding equal things to equal things, 
that the Refradions at K and H taken together, are equal 
to the Refractions at J and L taken together , and there- 
fore the two Rays being equally refradred have the fame 
Inclination to one another after Refradion which they had 
before, that is the Inclination of half a Degree anfwering 
to the Sun s Diameter. For fo great was the Inclination 
of the Rays to one another before Refradlion. So then, 
the length of the Image P T would by the Rules of VuU 
gar Opticks fubtend an Angle of half a Degree at the 
Prifm, and by confequence be equal to the breadth Vm -^ 
and therefore the Image would be round. Thus it would 
be were the two Rays X L J T and Y K H P and all the 
reft which form the Image P «» T >, alike Refrangible* 
And therefore feeing by Experience it is found that the 
Image is not round but about five times longer than 
broad, the Rays which going to the upper end P of the 
Image fuffer the greateft Refraction, muft be more Refran- 
gible than thofe which go to the lower end T , unlefs the 
inequality of Refraction be cafual. 

This Image or SpeCtrum P T was coloured, being red 
at its leaft rerraCted end T, and violet at its moft refraCted 
end P, and yellow green and blew in the intermediate 
fpaces. Which agrees with the firft Propofition, that Lights 
which differ in Colour do alfo differ in RefrangibiHty, 
The length of the Image in the foregoing Experiments I 
meafured from the fainteft and outmoft red at one end, to 
the fainteft and outmoft bjew at the other end. A/:^,:,^^^ , 

Exper, 4. In the Sun s beam which was propagated in- 
to the Room through the hole in the Window-fhut, at 
the diftance of fome Feet from the hole, I held the Prifm 
in fuch a pofture that its Axis might be perpendicular to 
diat beam. Then I looked through the Prifm upon the 

hole, 



J 



[23] 

hole, and turning the Prifm to and fro about its Axis to 
make the Image of the hole afcend and defcend, when be*- 
tween its two contrary Motions it feejned ftationary, I 
ftopt the Prifm that the Refractions on both fides of the 
refradling Angle might be equal to each other as in the 
former Experiment. In this Situation of the Prifm view- 
ing through it the faid hole, I obferved the length of its 
refra6ted image to be many times greater than its breadth,,, 
and that the moft refra<5led part thereof appeared violet, 
the leaft refra6led red, the middle parts blew green and 
yellow in order. The fame thing happened when I re*- 
moved the Prifm out of the Sun s Light , and looked 
through it upon the hole fliining by the Light of the 
Clouds beyond it. And yet if the Refra6lion were done 
regularly according to one certain Proportion of the Sines 
of Incidence and Refra(5lion as is vulgarly fuppofed, the 
r€fra<3:ed Image ought to have appeared round. 

So then, by thefe two Experiments it appears that in 
equal Incidences there is a confiderable inequality of Re- 
fradions : But vv^hence this inequality arifes, whether it be 
that feme of the incident Rays are refradte.d more and 
others lefs, conftantly or by chance, or that one and the 
fame Ray is by Refra6tion diftuAed, fhatiered, dilated, 
and as it were fplit and fpread into many diverging Rays, 
as Grimaldo fuppofes, does not yet appear by thefe Experi^ 
nients, but will appear by thofe that follow. 

Exper. 5 . Confidering therefore, that if in the third Ex- 
periment the image of the Sun fhould be drawn out into 
an oblong form, erther by a Dilatation of every Ray, or 
by any other cafual inequality of the Refractions, the fame 
cblong Image ^vouid by a (econd Refra6lion made Side- 
mzjs be drawn out as nmch in breadth by -the like Dila- 
itatioa 'of the Ray^-or othe»r ■cafeai i-n-e-Qiiaiky oftheRe^ 

frad;ionS: 



fraftions Sideways, I tried what would be the EfFeds of 
fuch a fecond Refraftion. For this end I ordered all things 
as in the third Experiment, and then placed a fecond Prilm 
immediately after the firft in a crofs Pofition to it, that it 
might again refradl the beam of the Sun's Light which 
came to it through the firft Prifm. In the firft Prilm this 
?beam was refracted upwards, and in the fecond Sideways. 
And I found that by the Refradtion of the fecond Prifm 
the breadth of the Image was not increafed, but its fupe- 
>rior part which in the firft Prifm fuffered the greater Re- 
fradion and appeared violet and blew, did again in the 
.fecond Prilm fuffer a greater Refraction than its inferior 
part, which appeared red and yellow , and this without 
any Dilation of the Image in breadth. 
#g. 14. Illujlration, Let S reprefent the Sun, F the hole in the 
Window, A B C the firft Prifm, D H the fecond Prifm, Y 
the round Image of the Sun made by a dired: beam of 
Lic^ht when the Prifms are taken away, P T the oblong 
Image of the Sun made by that beam paffing through the 
firft Prifm alone when the fecond Prifm is taken away, and 
ft the Image made by the crofs Refradlions of both 
Prifms together. Now if the Rays which tend towards 
the feveral Points of the round Image Y were dilated and 
ipread by the Refradion of the firft Prifm, fo that they 
fliould not any longer go in fingle Lines to fingle Points, 
but that every Ray being fpHt, fliattered, and changed 
from a Linear Ray to a Superficies of Rays diverging 
from the Point of Reftadion, and lying in the Plane of 
the Angles of Incidence and Refradion, they fhould 
go in thofe Planes to fo many Lines reaching almoft 
from one end of the Image P T to the other, and if 
that Image fliould thence become oblong : thofe Rays 
and their feveral parts tending towards the feveral Points of 

the 



[•25] 

the Image P T ought to be again dilated and fpread Side- 
ways by the tranfverfe Refradlion of the fecond Prifm , fo 
as to compofe a fourfcjuare Image, fuch as is reprefented 
at ^^7. For the better underftanding of which, let the hnage 
PT be diftinguiflied into five equal Parts PQK, KQ^RL, 
LRSM, MSVN, NVT. And by the fame irregularity 
that the Orbicular Light Y is by the Refra6lion of the firft 
Prifm dilated and drawn out into a long Image P T, the 
the Light P Q.K which takes up a Ipace of the fame length 
and breadth with the Light Y ought to be by the Refra- 
ction of the fecond Prifm dilated and drawn out into the 
long Image '^qkp-> ^nd the Light K Q_R L into the long 
Image kqrl, and the Lights LRSM, MSVN, NVT 
into fo many other long Images I r s m^ m s y 71^ 7iy tl ^ and 
all thefe long Images would compofe the fourfquare Image 
o-l. Thus it ought to be were every Ray dilated by Re- 
fradion, and fpread into a triangular Superficies of Rays 
diverging from the Point of Refradlion. For the fecond 
Refradion would fpread the Rays one way as much as the 
firfl: doth another , and fo dilate the Image in breadth as 
much as the firft doth in length. And the fame thing 
ought to happen, v/ere fome Rays cafually refradied more 
than others. But the Event is otherwife. The Image P T 
was not made broader by the Refradion of the fecond 
Prifm, but only became oblique, as 'tis reprefented itpt^ 
its upper end P being by the Refradion tranflated to a 
greater diftance than its lower end T. So then the Light 
which went towards the upper end P of the Imac^e, \^as, 
(at equal Incidences) more refraded in the feconcl Prifm 
than the Light which tended towards the lower end T, 
that is the blew and violet, than the red and yellow 5 and 
therefore was more Refrangible. The fame Light was by 
the Refradion of the firft Prifm tranflated further from the 

D place 



[2<5] 

place Y to which it tended before Refradlion 5 and there* 
Fore fufFered as well in the firft Prifm as in the fecond a 
greater Refradion than the reft of the Light, and by con- 
fequenee was more Refrangible than the reft^ even before 
its incidence on the firft Prifm. 
^' Sometimes I placed a third Prifm after the fecond, and 

fometimes alfo a fourth after the third , by all which the 
Image might be often refrad:ed fideways : but the Rays 
which were more refradlcd than the reft in the firft Prifm. 
were alfo more r€fra6led in all the reft, and that without 
any Dilatation of the Image fideways : and therefore thofe 
Rays for their conftancy of a greater Refraction are de- 
fer vedly reputed more Refrangible. 
Fig. 15. But that the meaning of this Experiment may more 
clearly appear, it is to be confidered that the Rays whick 
are equally Refrangible do fall upon a circle anfwering to 
the Sun s Difque. For this was proved in the third Experi- 
ment. By a circle I underftand not here a perfect Geo- 
metrical Circle, but any Orbicular Figure whofe length is 
equal to its breadth, and which, as to fenfe, may feem 
circular. Let therefore A G reprefent the circle which all 
the moft Refrangible Rays propagated from the whole 
Difque of the Sun, would illuminate and paint upon the 
oppofite Wall if they were alone 5 E L the circle which all 
the leaft Refrangible Rays would in like manner illuminate 
and paint if they were alone 3 B H, C J, D K, the circles 
which fo many intermediate forts of Rays would fuccef- 
fively paint upon the Wall, if they were fingly propagated 
firom the Sun in fucceiEve Order, the reft being always in- 
tercepted ^ And conceive that there are other intermediate 
Circles without number which innumerable other inter- 
mediate forts of Rays would fucceflively paint upon the 
Wall if the Sun fliould fucceflively emit every fort apart. 



[2?] 

And feeing the Sun emits all thefe forts at once, they muft 
all together illuminate and paint innumerable equal cir- 
cles, of all which, being according to their degrees of Re- 
frangibility placed in order in a continual fcries, that ob- 
long Spedrum P T is compofed which I defcribed in the 
third Experiment. Now if the Sun^s circular Image Y ficf. ]^h( ]^. 
which is made by an unrefra^fted beam of Light was by 
any dilatation of the fingle Rays, or by any other irregu- 
larity in the Refra6lion of the firft Prifm, converted into 
the Oblong Spedrum, P T : then ought every circle A G, 
B H, C J, <src. in that Spedrum, by the crofs Refra- 
(flion of the fecond Prifm again dilating or otherwife 
fcattering the Rays as before, to be in like manner drawn 
out and transformed into an Oblong Figure, and thereby 
the breadth of the Image P T would be now as much aug- 
mented as the length of the Image Y was before by the Re- 
fradion of the firft Prifm 5 and thus by the Refractions of 
both Prifms together would be form^ed a fourfquare Figure 
f'^t'] as I defcribed above. Wherefore fince the breadth of 
the Spedrum P T is not increafed by the Refradion fide- 
ways, it is certain that the Rays are not fplit or dilated, or 
otherways irregularly fcattered by that Refradrion, but 
that every circle is by a regular and uniform R.efra6l:ion 
tranflated entire into another place, as the circle A G by 
the greateft Refradion into the place ag^ the circle B H by 
a lefs Refradion into the place bh^ the circle C J by a Re- 
fradion ftill lefs into the place ci^ and fo of the reft 3 by 
which means a new Spedrum p t inclined to the former 
P T is in like manner compofed of circles lying in a 
right Line 5 and thefe circles muft be of the fame bignefs 
with the former, becaufe the breadths of all the Spe- 
dirums Y, P T and pt zt equal diftances from the PriiiTis 
are equal. 

D 2 I con- 



[28] 

I confidered further that by the breadth of the hole F 
through which the Light enters into the Dark Chamber^^ 
there is a Penumbra made in the circuit of the Spedlrum 
Y, and that Penumbra remains in the re6lilinear Sides of 
the Spectrums P T and pt, I placed therefore at that hole 
a Lens or Object- glafs of a Telefcope which miglit caft 
the Image of the Sun diftin6lly on Y without any Penum- 
bra at all, and found that the Penumbra of the Redili- 
near Sides of the oblong Spedrums P T and pt was alfo 
thereby taken away, fo that thofe Sides appeared as di- 
ftindly defined as did the Circumference of the firfl Image 
Y. Thus it happens if the Glafs of the Prifms be free 
from veins, atd their Sides be accurately plane and well 
polifiied without thofe numberlefs waves or curies which 
ufually arife from Sand-holes a little fmoothed in polifli- 
ing with Putty. If the Glafs be only well polifbed and 
free from veins and the Sides not accurately plane but a 
little Convex or Concave, as it frequently happens 5 yet 
may the three Spe6trums Y, P T and pt want Penumbras, 
but not in equal diftances from the Prifms. Now from 
this waht of Penumbras, I knew more certainly that every 
one of the circles was refra6ted according to feme moil 
regular, uniform, and conftant law. For if there were 
any irregularity in theRefradion, the right Lines A E and 
G L which all the circles in the Spedrum P T do touch, 
could not by that Refradlion be tranflated into the Lines 
a e and g I as difl:in(5t and ftraight as they were before, but 
there would arife in thofe tranflated Lines fome Penumbra 
or crookednefs or undulation, or other fenfible Perturba- 
tion contrary to what is found by Experience. Whatfo- 
cver Penumbra or Perturbation flhould be made in the 
circles by the crofs Refraction of the fecond Prifm , all 
that Penumbra or Perturbation would be confpicuous in 

the 



[29] 
the right Lines a e and g I which touch thofe circles. And 
therefore fince there is no fuch Penumbra or Perturbation 
in thofe right Lines there muft be none in the circles. 
Since the diftance between thofe Tangents or breadth of 
the Spedrum is not increafed by the Refrad;ions, the Dia- 
meters of the circles are not increafed thereby. Since thofe 
Tangents continue to be right Lines , every circle which 
in the firft Prifm is more or lefs refracted , is exadlly in 
the iame Proportion more or lefs refracted in the fecond. 
And feeing all thefe things continue to fucceed after the 
fame manner when the Rays are again in a third Prifm, 
and again in a fourth refradted Sideways, it is evident that 
the Rays of one and the fame circle as to their degree of 
Refrangibiiity continue always Uniform and Homogeneal 
to one another, and that thofe of feveral circles do differ 
in degree of Refrangibiiity, and that in fome certain and 
conftant Proportion. Which is the thing I was to prove. 

There is yet another Circumftance or two of this Ex-Fg. i6, 
periment by which it becomes ftill more plain and con- 
vincing. Let the fecond Prifm D H be placed not imme- 
ately after ^^ the firft, but at fome diftance from it 5 
Suppofe in the mid-way between it and the Wall on which 
the oblong Spedrum P T is caft, fo that the Light from 
the firft Prifm may fall upon it in the form of an oblong 
Spcdrum, ^7 Parallel to this fecond Prifm, and berefraded 
Sideways to form the oblong Spedrum p t upon the Wall. 
And you will find as before, that this Spedrum ft \s in- 
clined to that Spedrum P T, which the firft Prifm forms 
alone without the fecond 3 the blew ends P and f being fur- 
ther diftant from one another than the red ones T and tj 
and by confequence that the Rays which go to the blew 
end '^ of the Image ^^1 and which therefore fuffer the greateft 
Refraction in the firft Prifm, are again in the fecond Prifm 
more reiraded than the reft. The 



[30] 

'Fig, 17. The fame thing I try'd alfo by letting the Suns Light 
into a dark Room through two little round holes F and p 
made in the Window, and with two Parallel Prifms ABC 
and a0y placed at thofe holes ( one at each ) refradling 
thofe two beams of Light to the oppofite Wall of the 
Chamber, in fuch manner that the two coloured Images 
P T and MH which they there painted were joyned end to 
end and lay in one ftraight Line, the red end T of the 
one touching the blew end JB of the other. For if thefe 
two refradled beams were again by a third Prifm D H pla- 
ced croft to the two firft, refradied Sideways, and the Spe- 
d:rums thereby tranflated to fome other part of the Wall 
of the Chamber , fuppofe the Spedirum P T to p t and 

"^ulf jj'. the Spedlrum M N to in w, thefe tranflated Spe(ftrums p t 
and m n would not lie in one ftraight Line with their ends 
contiguous as before, but be broken off from one another 
and become Parallel, the blew end of the Image m n being 
by a greater Refra(5lion tranflated farther from its former 
place M T, than the red end t of the other Image p t from 
the fame place MT which puts the Propofition paft di- 
Ipute. And this happens v/hether the third Prifm D H be 
placed immediately after the two firft or at a great diftance 
from them , fo that the Light refracbed in the two firft 
Prifms be either white and circular, or coloured and ob- 
long when it falls on the third, 

Exper. 6. In the middle of tw^o thin Boards I made 
round holes a third part of an Inch in Diameter, and in 
the Window-iliut a much broader hole, being made to let 
into my darkned Chamber a large beam of the Sun's 
Light 5 I placed a Prifm behind the Shut in that beam to 
refradt it towards the oppofite Wall, and clofe behind the 
Prifm I fixed one of the Boards, m fuch manner that the 
middle of the refraded Light might pafs through the hole 

made 



made in it, and the reft be intercepted by the Board. 
Then at the diftance of about twelve Feet from the firft 
Board I fixed the other Board, in fuch manner that the 
middle of the refraded Light which came through the hole 
in the firft Board and fell upon the oppofite Wall might 
pafs through the hole in this other Board, and the reft be- 
ing intercepted by the Board might paint upon it the co- 
loured Spedrum of the Sun. And clofe behind this Board 
I fixed another Prifm to refrad: the Light which came 
through the hole. Then I returned fpeedily to the firft 
Prifm, and by turning it flowly to and fro about its Axis, 
I caufed the Image which fell upon the fecond Board to 
move up and dov/n upon that Board, that all its parts 
might fucceffively pafs through the hole in that Board and 
fall upon the Prifm behind it. And in the mean time, I 
noted the places on the oppofite Wall to which that Li8;ht 
after its Refrad:ion in the fecond Prifm did pafs 5 and by 
the difference of the places I found that the Light which 
being moft refradled in the firft Prifm did go to the blew 
end of the Image, was again more refrad:ed in the fecond 
Prifm than the Light which went to the red end of that 
Image, which proves as well the firft Propofition as the 
fecond. And this happened whether the Axis of the two 
Prifms were parallel, or inclined to one another and to the 
H©rizon in any given Angles. 

Illuftration, Let F be the wide hole in the Window-fliut, p^^ i g^ 
through which the Sun fliines upon the firft Prifm ABC, 
and let the refraded Light fall upon the middle of the 
Board D E, and the middle part of that Light upon the 
hole G made in the middle of that Board. ~ Let this tra- 
jededpart of the Light fall again upon the middle of the 
fecond Board d e and there paint fuch an oblong coloured 
Image of the Sun as was defcribed in the third Experiment. 

By 



[32] 

By turning the Prifm ABC flowly to and fro about its 
Axis this Image will be made to move up and down the 
Board d e, and by this means all its parts from one end to 
the other may be made to pafs fucceflively through the 
hole g which is made in the middle of that Board. In the 
mean while another Prifm a b c is to be fixed next after 
that hole^ to refradl the trajed:ed Light a fecond time. 
And thefe things being thus ordered, I marked the places 
M and N of the oppofite Wall upon which the refracfled 
Light fell,and found that whilfl: the two Boards and fecond 
Prifm remained unmoved, thofe places by turning the firft 
Prifm about its Axis were changed perpetually. For when 
the lower part of the Light which fell upon the fecond 
Board d e was caft through the hole g it went to a lower 
place M on the Wall , and when the higher part of that 
Light was call: through the fame hole^, it went to a higher 
place N on the Wall, and when any intermediate part of 
the Light was cafl; through that hole it went to fome place 
on the Wall between M and N. The unchanged Pofition 
of the holes in the Boards, made the Incidence of the Rays 
upon the fecond Prifm to be the fame in all cafes. And 
yet in that common Incidence fome of the Rays were more 
refracted and others lefs. And thofe were more refradled 
in this Prifm which by a greater Refraction in the firft 
Prifm were more turned out of the way, and therefore for 
their conftancy of being more refiraCled are defervedly cal- 
led more Refrangible. 

Exper. 7. At two holes made near one another in my 
Window-flhut I placed two Prifms , one at each, which 
might caft upon thi oppofite Wall ( after the manner of 
the third Experiment ) two oblong coloured Images of the 
Sun. And at a little diftance from the Wall I placed a 
long flender Paper with flraight and parallel edges, and 

ordered 



C33 3 

ordered tlie Prifms and Paper fo, that the red Colour of 
one Image might fall diredly upon one half of the Paper, 
and the violet colour of the other Image upon the other 
half of the fame Papery fo that the Paper appeared of two 
Colours , red and violet , much after the manner of the 
painted Paper in the firft and fecond Experiments. Then 
with a black Cloth I covered the Wall behind the Paper, 
that no Light might be refleded from it to difturb the 
Experiment, and viewing the Paper through a third Prifm < 
held parallel to it, I faw that half of it which was illumi- 
nated by the Violet-light to be divided from the other 
half by a greater Refradion, efpecially when I went a good 
way off from the Paper. For when I viewed it too near 
at hand, the two halfs of the Paper did not appear fully 
divided from one another , but feemed contiguous at one 
of their Angles like the painted Paper in the firft Expe- 
riment. Which alfo happened when the Paper was too 
broad. 

Sometimes inftead of the Paper I ufed a white Thred, 
and this appeared through the Prifm divided into two Pa- 
rallel Threds as is reprefented in the 19th Figure, where Fig-. 19. 
D G denotes the Thred illuminated with violet Light 
from D to E and with red Light from F to G, and d e fg 
are the parts of the Thred feen by RefracSiion. li one hali 
of the Thred be conPcantly illuminated with red, and the 
other half be illuminated with all the Colours fucceffively, 
(which may be done by caufing one of the Prifms to be 
turned about its Axis whilft the other remains unmoved) 
this other half in viewing the Thred through the Prifm, 
will appear in a continued right Line with the firft half 
when illuminated with red , and begin to be a little divi- 
ded from it v/hen illuminated with Orange, and remove 
further from it when illuminated with Yellow, and ft-ill 

E further 



[34] 

further when with Green, and further when with Blew, and 
20 yet further off when illuminated with Indigo, and fur* 
^ theft when with deep Violet. Which plainly flhews, that 
the Lights of feveral Colours are more and more Refran- 
gible one than another, in this order of their Colours, Red, 
Orange, Yellow, Green, Blew, Indigo, deep Violet 3 and 
fo proves as well the firft Propofition as the fecond. 
F^^. 17. I caufed alfo the coloured Spedrums PT and MN 
made in a dark Chamber by the Refradions of two Prifms 
to lye in a right Line end to end, as was defcribed above 
in the fifth Experiment, and viewing them through a third 
Prifm held Parallel to their length, they appeared no longer 
in a right Line, but became broken from one another, as 
they are reprefented at pt and mri, the violet end m of the 
Spedlrum m n being by a greater Refradlion tranflated 
further from its former place M T than the red end^ of the 
other Spedrum p t. 
^i(r. 20. I further caufed thofe two Spedlrums P T and M N to 
*^ become co-incident in an inverted order of their Colours, 

the red end of each falling on the violet end of the other, 
as they are reprefented in the oblong Figure P T M N 5: 
and then viewing them through a Prifm D H held Paral- 
lel to their length, they appeared not co-incident as when 
viewed with the naked Eye , but in the form of two di- 
ftind: Spedlrums p t and m n crofling one another in the 
middle after the manner of the letter X. Which flhews 
that the red of the one Sped:rum and violet of the other, 
which were co-incident at PN and MT, being parted 
from one another by a greater Refradion of the violet to 
p and m than of the red to n and f, do differ in degrees of 
Refrangibility. 

I illuminated alfo a little circular piece of white Paper 
all over with the Lights of both Prifms intermixed, and 

when. 



35] 

when it was illuminated with the red of one Spedlrum and 
deep violet of the other , fo as by the mixture of thofc 
Colours to appear all over purple , I viewed the Paper, 
firft ai a lefs diftance , and then at a greater , through a 
third Prifm 5 and as I went from the Paper, the refracted 
Image thereof became more and more divided by the un- 
equal Refra6tion of the two mixed Colours, and at length 
parted into two diftind: Images, a red one and a violet one, 
whereof the violet was fijrtheft from the Paper, and there- 
fore fuftered the greateft Pvefrad:ion. And when that Prifm 
at the Window which caft the violet on the Paper was ta- 
ken away,iiie violet Image difappeared^ but when the other 
Prilm was taken away the red vanifhed : which fliews that 
thefe two Images were nothing elfe than the Lights of the 
two Prifms which had been intermixed on the purple Pa- 
per, but were parted again by their unequal Refractions 
made in the third Prifm through which the Paper was 
viewed. This alfo was obfervable that if one of the 
Prifms at the Window, fuppofe that which caft the violet 
on the Paper, was turned about its Axis to make all the 
Colours in this order, Violet, Indigo, Blew, Green, Yel- 
low, Orange, Red, fall fucceffively on the Paper from that 
Prifm, the violet Image changed Colour accordingly, and 
in changing Colour came nearer to the red one, until when 
it was alfo red they both became fully co-incident. 

I placed alfo two paper circles very near one another, 
the one in the red Light of one Prifm, and the other in 
the violet Light of the other. The circles were each of 
them an hich in Diameter, and behind them the Wall was 
dark that the Experiment might not be difturbed by any 
Light coming from thence. Thefe circles thus illuminated, 
I viewed through a Prifm fo held that the Refradtion might 
be made towards the red circle , and as I went from them 

E 2 they 



they came nearer and nearer together, and at length be-^ 
came co-incident 3 and afterwards when I went ftill further 
off, they parted again in a cotitrary order, the violet by a 
greater Refra<flion being carried beyond the red. 

Exper. 8. In Summer when the Sun's Light ufes to 
be ftrongeft, I placed a Prifm at the hole of the Window- 
lliut, as in the third Experiment, yet fo that its Axis might 
be Parallel to the Axis of the World, and at the oppofite 
Wall in the Sun's refraded Light, I placed an open Book. 
Then going Six Feet and two Inches from the Book, I 
placed there the abovementioned Lens,by which the Light 
reflected from the Book might be made to converge and 
meet again at the diftance of fix Feet and two Inches be- 
hind the Lens , and there paint the Species of the Book 
upon a Hieet of white Paper much after the manner of the 
fecond Experiment. The Book and Lens being made faft, 
I noted the place where the Paper was, when the Letters 
of the Book, illuminated by the fulleft red Light of the 
Solar Image falling upon it, did caft their Species on that 
Paper moft diftindly 3 And then I ftay'd till by the Mo* 
tion of the Sun and confequent Motion of his Image on 
the Book, all the Colours from that red to the middle of 
the blew pafs'd over thofe Letters 5 and when thofe Letters 
were illuminated by that blew, I noted again the place of 
the Paper when they caft their Species moft diftindly upon 
it : And I found that this laft place of the Paper was nearer 
to the Lens than its former place by about two Inches and 
an half, or tv/o and three quarters. So much fooner there- 
fore did the Light in the violet end of the Image by a grea- 
ter Pvefrad:ion converge and meet , than the Light in the 
red end. But in trying this the Chamber was as dark as I 
could make it. For if thefe Colours be diluted and weak- 
ned by the mixture of any adventitious Light, the diftance 

between 



[ 37 ] 

between the places of the Paper will not be fo great. This 
diftance in the fecond Experiment where the Colours of 
natural Bodies were made ufe of, was but an Inch and a 
half, by reafon of the imperfedion of thofe Colours. Here 
in the Colours of the Prifm , which are manifeftly more 
full, intenfe, and lively than thofe of natural Bodies, the 
diftance is two Inches and three quarters. And were the 
Colours ftill more full , I queftion not but that the di» 
ftance would be confiderably greater. For the coloured 
Light of the Prifm, by the interfering of the Circles de- 
fcribed in the i ith Figure of the fifth Experiment, and alfo 
by the Light of the very bright Clouds next the Sun's 
Body intermixing with thefe Colours, and by the Light 
fcattered by the inequalities in the polifli of the Prifm, was 
fo very much compounded, that the Species which thofe 
faint and dark Colours, the Indigo and Violet, caft upon 
the Paoer vvxre not diftindl enough to be well obferved. 

Exper. p. A Prifm, whofe two Angles at its Bafe were 
equal to one another and half right ones, and the third 
a right one, I placed in a beam of the Sun's Light let in- 
to a dark Chamber through a hole in the Window-fhut 
as in the third Experiment. And turning the Prifm flowly 
about ics Axis until all the Light which went through one 
of its Angles and was refracted by it began to be refleded 
by its Bafe , at which till then it went out of the Glafs, 
I obferved that thofe Rays which had fuffered the greateft 
Refraction were fooner reflected than the reft. I conceived 
therefore that thofe Rays of the refledled Light, which 
were moft Refrangible, did firft of all by a total Reflexion 
become more copious in that Light than the reft , and 
that afterwards the reft alfo, by a total Reflexion, be- 
came as copious as thefe. To try this , I made the re- 
fleded Light pafs through another Prifm, and being refra- 

ded 



[38] 

ded by it to fall afterwards upon a fbeet of white Paper 
placed at fome diftance behind it, and there by that Re- 
fradion to paint the ufual Colours of the Prifm. And 
tlien caufing the firft Prifm to be turned about its A:>cis as 
above, I obferved that when thofeRays which in this Prifm 
had fuffered the greateft Refradion and appeared of a blew 
and violet Colour began to be totally refleded , the blew 
and violet Light on the Paper which was moft refraded 
in the fecond Prifm received a fenfible increafe above that 
of the red and yellow, which was leaft refraded 5 and 
afterwards when the reft of the Light which was green, 
yellow and red began to be totally refleded in the firft 
Prifm, the hghtofthofe Colours on the Paper received as 
great an increafe as the violet and blew had done before. 
Whence 'tis manifeft, that the beam of Light refleded by 
the Bafe of the Prifm, being augmented firft by the more 
Refrangible Rays and afterwards by the lefs Refrangible 
ones, is compounded of Rays differently Refrangible. 
And that all fuch refledled Light is of the fame Nature 
with the Sun's Light, before its Incidence on the Bafe of 
the Prifm, no Man ever doubted : it being generally al- 
lowed, that Light by fuch Reflexions fuffers no Alteration 
in its Modifications and Properties. I do not here take 
notice of any Refradions made in the Sides of the firft 
Prifm, becaufe the Light enters it perpendicularly at the 
firft Side, and goes out perpendicularly at the fecond Side, 
and therefore fuffers none. So then, the Sun's incident 
Light being of the fame temper and conftitution with his 
emergent Light, and the bft being compounded of Rays 
differently Refrangible , the firft muft be in like manner 
compounded. 
Fi^. 1 1 . Illuftration. In the 1 1 th Figure, A B C is the firft Prifm, 
B C its Bafe, B and C its equal Angles at the Bafe, each 

of 



[39] 

of 45 degrees, A its Redangular Vertex, F M a beam of 
the Sun's Light let into a dark Room through a hole B 
one third part of an Inch broad, M its Incidence on theBafe 
of the Prifm^M G a lefs refraded Ray, M H a more refra6t- 
ed Ray, M N the beam of Light refle6led from the Bafe , 
V X Y the fecond Prifm by which this beam in paffing 
through it is refrad:ed, N t the lefs refracted Light of this 
beam, and N p the more refracted part thereof. When the 
firft Prifm A B C is turned about its Axis according to the 
order of the Letters ABC, the Rays M H emerge more 
and more obliquely out of that Prifm, and at length after 
their moft oblique Emergence are refle6led towards N, 
and going on to p do increafe the number of the Rays N^^ 
Afterwards by continuing the motion of the firft Prifm, the 
Rays M G are alfo reflected to N and increafe the number of 
the Rays N t. And therefore the Light M N admits into 
its Compofition, firft the more Refrangible Rays, and then 
the lefs Refrangible Rays, and yet after this Compofition 
is of the fame Nature with the Sun's immediate Light F M, 
the Reflexion of the fpecular Bafe B C caufing no Altera- 
tion therein. 

Exper. I o. Two Prifms, which were alike in fliape, I 
tied fo together, that their Axes and oppofite Sides being 
Parallel, they compofed a Parallelopiped,. And, the Sun 
fliining into my dark Chamber through a little hole in the 
Window-fhut, I placed that Parallelopiped in his beam at 
fome diftance from the hole, in fuch a pofture that the Axes 
of the Prifms might be perpendicular to the incident Rays, 
and that thofe Rays being incident upon the firft Side of 
one Prifm, might go on through the two contiguous Sides 
of both Prifms, and emerge out of the laft Side of the fe- 
cond Prifm. This Side being Parallel to the firft Side of 
the firft Prifm 5 caufed the emerging Light to be Parallel 

to 



[ 4° ] 

to the Incident. Then, beyond thefe two Prifms I placed 
a third, which might refrad that emergent Light, and by 
that Refradion caft the ufual Colours of the Prifm upon 
the oppofite Wall, or upon a (Tieet of white Paper held at 
a convenient diftance behind the Prifm for that refradled 
Light to fall upon it. After this I turned the Parallelopiped 
about its Axis, and found that when the contiguous Sides 
of the two Prifms became fo obHque to the incident Rays 
that thofe Rays began all of them to be refie6ted , thofe 
Rays which in the third Prifm had fuffered the greatefi; Re- 
fraction and painted the Paper with violet and blew, were 
firfl: of all by a total Reflexion taken out of the tranfmitted 
Light, the reft remaining and on the Paper painting their 
Colours of Green, Yellow, Orange, and Red as before 3 
and afterwards by continuing the motion of the two Prifms, 
the reft of the Rays alfo by a total Reflexion vaniflied in 
order, according to their degrees of Refrangibility. The 
Licrht therefore which emerged out of the two Prifms is 
compounded of Rays differently Refrangible , feeing the 
more Refrangible Rays may be taken out of it v/hile the 
lefs Refrangible remain. But this Light being trajedted 
only through the Parallel Superficies of the two Prifms, if 
it fuffered any change by the Refradion of one Superficies 
it loft that impreffion by the contrary Refradion of the 
other Superficies, and fo being reftored to its priftine con- 
ftitution became of the fame nature and condition as at firft 
before its Incidence on thofe Prifms 3 and therefore, before 
its Incidence, was as much compounded of Rays differently 
Refrangible as afterwards. 
Fig. 11. Iliuflration. In the nth Figure ABC and BCD are the 
the two Prifms tied together in the form of a Parallelo- 
piped, their Sides BC and CB being contiguous, and 
their Sides A B and C D Parallel. And H J K is the third 

Prifm, 



C4-0 

Prifm, by which the Sun's Light propagated through tlie 
hole F into the dark Chamber, and there paffing through 
thofe fides of the Prifms AB, BC, CB and CD, is refra- 
died at O to the white Paper PT, falling there partly upon 
P by a greater Refradiion, partly upon T by a lefs Refra- 
dlion, and partly upon R and other intermediate places by 
intermediate Refractions. By turning the Parallelopiped 
ACBD about its Axis, according to the order of the Let- 
ters A,C,D,B, at length when the contiguous Planes BC 
and CB become fufficiently oblique to the Rays F M, 
which are incident upon them at M, there will vaniflh to- 
tally out of the refraded Light OPT, firft of all the moft 
refraded Rays O P, (the reft OR and O T remaining as 
before) then the Rays O R and other intermediate ones, 
and laftly, the leaft refracted Rays O T. For when the 
Plane B C becomes fufficiently oblique to the Rays inci- 
dent upon it, thofe Rays will begin to be totally reflect- 
ed by it towards N 5 and firft the moft Refrangible Rays 
will be totally reflected (as was explained in the preceding 
experiment) and by confequence muft firft difappear at P, 
and afi:erwards the reft as they are in order totally reflect- 
ed to N, they muft difappear in the fame order at R and 
T. So then the Rays which at O fuffer the greateft Re- 
fraction, may be taken out of the Light M O whilft the reft 
of the Rays remain in it, and therefore that Light MO is 
Compounded of Rays diiferently Refrangible. And be- 
caufe the Planes A B and C D are parallel, and therefore 
by equal and contrary RefraCtions deftroy one anothers 
Effects, the incident Light F M muft be of the fame kind 
and nature with the emergent Light M O, and therefore 
doth alfo confift of Rays differently Refrangible. Thefe 
two Lights FM and ?vIO, before the moft reirangible Rays 
are feparated out of the emergent Light M O agree in Co- 

F lour. 



C4^] 

lour, and in all other properties fo far as my obfervation 
reaches, and therefore are defervedly reputed of the fame 
Nature and Conftitution, and by confequence the one is 
compounded as well as the other. But after the moft Re* 
frangible Rays begin to be totally refleded, and thereby 
feparated out of the emergentLightMO,that Light changes 
its Colour from white to a dilute and faint yellow, a pretty 
good orange, a very full red fucceffively and then totally 
vaniflbes. For after the moft Refrangible Rays which paint 
the Paper at P Vvdth a Purple Colour, are by a total re- 
flexion taken out of the Beam of hght M O, the reft of 
the Colours which appear on the Paper at R and T being 
mixed in the light MO compound there a faint yellow^ 
and after the blue and part of the green which appear on 
the Paper between P and R are taken away, the reft which .- 
appear between R and T (that is the Yellow, Orange, Red 
and a little Green) being mixed in the Beam M O com- 
pound there an Orange 5 and when all the Rays are by re- 
flexion taken out of the Beam MO, except the leaft Refran- 
gible, which at T appear of a full Red, their Colour is 
the fame in that Beam MO as afterwards at T, the Re- 
fraction of the Prifm HJK ferving only to feparate the 
differently Refrangible Rays, without making any alteration 
in their Colours, as (hall be more fully proved hereafter. 
All which confirms as well the firft Propofition as the fe- 
cond. 

Scholium. If this Experiment and the former be conjoyned 
w. 11* and made one, by applying a fourth Prifm VXY to re- 
fradl the reflected Beam M N towards tp^ the conclufion 
will be clearer. For then the light N^ which in the 4th 
Prifm is more refracted, will become fuller and ftronger 
when the Light O P, which in the third Prifm HJK is 
more refraded, vanifhes at P 3 and afterwards when the lefs 

refrs^ded 



I43] 

refra(fled Light O T vaniflies at T^the lefs refraded Light 
Nf will become encreafed whilft the more refraded Light 
at p receives no further encreafe. And as the trajeded 
Beam M O in vanifliing is always of fuch a Colour as 
ought to refult from the mixture of the Colours which 
fall upon the Paper PT, fo is the refleded Beam MN al- 
ways of fuch a Colour as ought to refult from the mix- 
ture of the Colours which fall upon the Paper p t. For 
when the moft refrangible Rays are by a total Reflexion 
taken out of the Beam M O, and leave that Beam of an 
Orange Colour, the excefs of thofe Rays in the refleded 
Light, does not only make the Violet, Indigo and Blue at 
p more full, but alfo makes the Beam M N change from 
the yellowifli Colour of the Sun's Light, to a pale white in- 
clining to blue, and afterward recover its yellowifli Co- 
lour again, fo foon as all the reft of the tranfmitted light 
MOT is refleded. 

Now feeing that in all this variety of Experiments, 
whether the trial be made in Light refleded, and that either 
from natural Bodies, as in the firft and fecond Experiment, 
or Specular, as in the Ninth 3 or in Light refiaded, and 
that either before the unequally refraded Rays are by di- 
verging feparated from one another, and loflng their white- 
nefs which they have altogether, appear feverally of feve- 
ral Colours, as in the fifth Experiment 5 or after they are 
feparated from one another, and appear Coloured as in the 
fixth, feventh, and eighth Experiments 3 or in Light tra- 
jeded through Parallel fuperficies, deftroying each others 
EfFeds as in the i oth Experiment 3 there are always found 
Rays, which at equal Incidences on the fame Medium fuf- 
fer unequal Refradions, and that without any Iplitting or 
dilating of fingle Rays, or contingence in the inequality 
of the Refradions, as is proved in the iifh and fixth Ex- 

F 2 -^^^'iments ; 



[44l 

periments 3 and feeing the Rays which differ in Refrangibi^ 
lity may be parted and forted from one another, and that 
cither by ReFra6lion as in the third Experiment, or by Re- 
flexion as in the tenth^ and then the feveral forts apart at 
equal Incidences fuffer unequal Refra6lions, and thofe forts^ 
are more refraded than others after feparation, which werer 
more refraded before it, as in the fixth and following Ex- 
periments, and if the Sun's Light be traje6led through three 
or more crofs Prifms fucceffively, thofe Rays which in the 
firft Prifm are refracfted more than others are in all the fol- 
lowing Prifms, refradred more then others in the fame rate 
and proportion, as appears by the fifth Experiment 3 it's 
manifeft that the Sun's Light is an Heterogeneous mixture of 
Rays, fome of which are conftantly more Refrangible then 
others, as was to-be propofed. 

T ROT. III. Theor. III. 

T^be Suns Light conftfts of ^ys differing in ^flexibility., and 
thofe ^ys are more ^flexible than others which are more (%- 
frangible. 

^ I ^HIS is manifeft by the ninth and tenth Experi- 
I ments : For in the ninth Experiment, by turning, 
the Prifm about its Axis, until the Rays within it which in 
going out into the Air were refraded by its Bafe, became 
lb oblique to that Bafe, as to begin to be totally reflected 
thereby 5 thofe Rays became firft of all totally refleded, 
which before at equal Incidences with the reft had fuffered 
the greateft Refradion. And the fame thing happens in 
the Reflexion made by the common Bafe of the two Prifms 
in the. tenth Experimentc 



[45] 
V ROV. IV. Prob. I. 

To feparate from one another the Heterogeneous ^ys of 

Compound Light, 




"^HE Heterogeneous Rays are in fome meafure fepa- 

rated from one another by the Refraction of the 

Prifm in the third Experiment, and in the fifth Experiment 
by taking away the Penumbra from the Re6tiHnear fides of 
the Coloured Image, that feparation in thofe very Rectili- 
near fides or ftraight edges of the Image becomes perfect. 
But in all places between thofe rectilinear edges, thofe in- 
numerable Circles there defcribed, which are feverally illu- 
minated by Homogeneral Rays, by interfering with one 
another, and being every where commixt, do render the 
Light fufficiently Compound. But if thefe Circles, whilft 
their Centers keep their diftances and pofitions, could be 
made lels in Diameter, their interfering one with another 
and by confequence the mixture of the Heterogeneous 
Rays would be proportionally diminiflied. In the 2 3th'Fg. 23. 
Figure let AG, B H, CJ, D K, EL, F M be the Circles 
which fo many forts of Rays flowing from the fameDifque 
of the Sun, do in the third Experiment illuminate 3 of all 
which and innumerable other intermediate ones lying in a 
continual Series between the two Redilinear and Parallel- 
edges of the Sun's oblong Image P T, that Image is com- 
pofed as was explained in the fifth Experiment. And let' 
agj bhy cij dk^j el ^ fm be fo many lefs Circles lying in 
a like continual Series between two Parallel right Lines af 
and ^ m with the fame diftances between their Centers, 
and illuminated by the fame forts of Rays, that is the 
Circle ag with the fame fort by which the correfponding 

Circle 



Circle A G was illuminated, and the Circle bh with the fame M 
fort by which the correfponding Circle BHwas illuminated, ) 
and the reft of the Circles c i, dk^ el, f)n refpedtively, 
with the fame forts of Rays by which the feveral corre- 
fponding Circles CJ, D K, EL, FM v/ere illuminated. 
In the Figure P T compofed of the greater Circles, three 
of thofe Circles AG, B H, C J, are (b expanded into one 
another, that the three forts of Pvays by which thofe Cir- 
cles are illaminated, together with other imiamerable forts 
of intermediate Rays, are mixed at Q. R in the middle of 
the Circle B H. And the like mixture happens through- 
out almoft the whole length of the Figure P T. But in 
the Figure p t compofed of the lefs Circles, the three lefs 
Circles ag^ hh^ c i, which anfwer to thofe three greater, do 
not extend into one another 5 nor are there any where 
mingled fo much as any two of the three forts of Rays 
by which thofe Circles are illuminated, r.nd which in the 
Figure P T are all of them intermingled at B H. 

Now he that fliall thus confider it, will eafily underftand 
that the mixture is diminiflhed in the fame Proportion 
with the Diameters of the Circles. If the Diameters of 
the Circles whilft their Centers remain the fame, be made 
three times lefs than before, the mixture will be alfo three 
times lefs 5 if ten times lefs, the mixture will be ten times 
lefs, and fo of other Proportions. That is, the mixture 
of the Rays in the greater Figure P T will be to their mix- 
ture in the lefs p /•, as the Latitude of the greater Figure is 
to the Latitude of the lefs. For the Latitudes of thefe Fi- 
gures are equal to the Diameters of their Circles. And 
hence it eafily follows, that the mixture of the Rays in the 
refracted Spedrum ^ f is to the mixture of the Rays in the 
dire6t and immediate Light of the Sun, as the breadth of 
that Spedrum is to the difference between the length and 
breadth of the fame Spedrum. <]ft^Ad7J:J^^:07iJ£<^^i So 



[47] 

So then, if we would diminifh the mixture of the Rays, 
w€ are to diminifh the Diameters of the Circles. Now 
thefe would be diminifh ed if the Sun's Diameter to which 
they anfwer could be made lefs than it is^ or (which comes 
to the fame purpofe) if without Doors, at a great diftance 
from the Prifm towards the Sun, fome opake body were 
placed, with a round hole in the middle of it, to intercept 
all the Sun s Light, excepting fo much as coming from 
the middle of his Body could pafs through that hole to 
the Prifm. For fo the Circles AG, BH and the reftj 
would not any longer anfwer to the whole Difque of the 
Sun , but only to that part of it which could be feen 
from the Prifm through that hole, that is to the apparent 
magnitude of that hole viewed from the Prifm. But that 
thefe Circles may anfwer more diftindlly to that hole a 
Lens is to be placed by the Prifin to caft the Image of the 
hole, (that is, every one of the Circles A G, B H, ^c.) di- 
ftindly upon the Paper at P T, after fuch a manner as by 
a Lens placed at a Window the Species of Objeds abroad 
are caft diftindlly upon a Paper within the Room, and the 
Redilinear Sides of the oblong folar Image in the fifth 
Experiment became difl;in(5i: without any Penumbra. If 
this be done it will not be neceffary to place that hole 
very far off, no not beyond the Window. And therefore 
inflead of that hole, I ufed the hole in the Window-fhut 
as follows. 

Exper. 1 1 . In the Sun's Light let into my darkned 
Chamber through a fmall round hole in my Window^ 
fhut, at about i o or 12 Feet from the Window, I placed 
a Lens , by which the Image of the hole might be di- 
ftindly caft upon a fheet of white Paper, placed at the 
diftance of fix, eight, ten or twelve Feet from the Lens. 
For according to the difference of the Lenfes I ufed various 

diftances, 



[48 

diftances , which I think not worth the while to defcrrbe. 
Then immediately after the Lens I placed a Prifm, by 
which the traje6ted Light might be refradled either up- 
wards or £deways, and thereby the round Image which 
the Lens alone did caftupon the Paper might be drawn 
out into a long one with Parallel Sides , as in the third 
Experiment. This oblong Image I let fall upon another 
Paper at about the fame diftance from the Prifm as be- 
fore, moving the Paper either towards the Prifm or from 
it, until I found the jufl: diftance where the Redilinear 
Sides of the Image became moft diftind:. For in this cafe 
the circular Images of the hole which compofe that Image 
after the fame manner that the Circles ag^ bh^ ci^ 8cc. do 
ft- 2 7. the Figure p f , were terminated moft diftindily without any 
Penumbra, and therefore extended into one another the 
leaft that they could, and by confequence the mixture of 
the Heterogeneous Rays was now the leaft of all. By this 
F/o-. 2^5 means I ufed to form an oblong Image (fuch as is pt) of 
and 24. circular Images of the hole (fuch as are ag, bh^ ci^ &c.) 
and by ufing a greater or lefs hole in the Window-ftiut, I 
made the circular Images ag^ bh^ c i, &c. of which it was 
formed, to become greater or lefs at pleafure, and thereby 
the mixture of the Rays in the Image pt to be as much 
or as little as I defired. 
Fk. 24. Illujiration. In the 24th Figure, F reprefents the circular 
hole in the Window-fliut, MN the Lens whereby the 
Image or Species of that hole is caft diftin6lly upon a 
Paper at J, ABC the Prifm whereby the Rays are at their 
emerging out of the Lens refracted from J towards ano- 
ther Paper at p f , and the round Image at J is turned into 
an oblong Image p t falling on that other Paper. This 
Image p t confifts of Circles placed one after another in a 
Reftilinear order^ as was fufficiently explained in the fifth 

Experiment 5 



[49] 

Experiment 3 and thefe Circles are equal to the Circle I, 
and confequently anfwer in Magnitude to the hole F 5 and 
therefore by diminifliing that hole they may be at pleafurc 
diminiflied , whirft their Centers remain in their places. 
By this means I made the breadth of the Image ^ t to be 
forty times, and fometimes fixty or feventy times lefs than 
its length. As for inftance, if the breadth of the hole F 
be ^ of an Inch, and MF the diftance of the Lens from 
the hole be 1 1 Feet 5 and if p B or pM the diftance of 
the Image pt from the Prifm or Lens be 10 Feet, and the 
refrading Angle of the Prifm be 62 degrees, the breadth 
of the Image p t will be ~ of an Inch and the length about 
fix Inches, and therefore the length to the breadth as 72 
to I, and by confequence the Light of this Image 71 times 
lefs compound than the Sun's dired: Light. And Light 
thus far Simple and Homogeneal , is fufficient for trying 
all the Experiments in this Book about fimple Light. For 
the compofition of Heterogeneal Rays is in this Light fo 
little that it is fcarce to be difcovered and perceived by 
fenfe, except perhaps in the Indigo and Violet 3 for thefe 
being dark Colours, do eafily fuffer a fenfible allay by that 
little fcatterincr Light which ufes to be refraded irrep^ularlv 
by the inequaiiteis of the Prijfin. 

Yet inftead of the circular hole F, 'tis better to fubfti- 
tute an oblong hole fliaped like a long Parallelogram 
with its length Parallel to the Prifm ABC. For if this 
hole be an Inch or two long, and but a tenth or twentieth 
part of an Inch broad or narrower : the Light of the-Imao^e 
p t will be as Simple as before or fimpler, and the Image 
will become much broader, and therefore more fit to have 
Experiments tried in its Light than before. 

Inftead of this Parallelogram-hole may be fubftituted a 
Triangular one of equal Sides, whofe Bafe for inftance is 

G about 



about the tenth part of an Inch, and its height an Inch or 
more. For by this means , if the Axis of the Prifm be 
Parallel to the Perpendicular of the Triangle , the Image 
Fig. ly pt will now be formed of Equicrural Triangles ag^ bh, ciy 
dk^j el^ f m^ Sec, and innumerable other intermediate ones 
anfwering to the Triangular hole in fhape and bignefs, and 
lying one after another in a continual Series between two 
Parallel Lines af zndgrn. Thefe Triangles are a little 
intermingled at their Bafes but not at their Vertices, and 
therefore the Light on the brighter fide af of the Image 
where the Bafes of the Triangles are is a little compounded, 
but on the darker fide ^ w is altogether uncompounded, 
and in all places between the fides the Compofition is 
Proportional to the diftances of the places from that ob- 
fcurer fide g m. And having a Spe6trum p t of fuch a 
Compofition, we may try Experiments either in its ftronger 
and lefs fimple Light near the fide af or in its weaker 
and fimpler Light near the other fide / m, as it fliall fe^n 
moft convenient. 

But in making Experiments of this kind the Chamber 
ought to be made as dark as can be, leaft any forreign 
Light mingle it felf with the Light of the Spedlrum p f, 
and render it compound 3 efpecially if we would try Ex- 
periments in the more fimple Light next the fide g ni of 
the Spedlrumj which being fainter, will have a lefs Pro- 
portion to the forreign Light, and fo by the mixture of 
that Light be more troubled and made more compound. 
The Lens alfo ought to be good, fuch as may ferve for 
Optical Ufes, and the Prifm ought to have a large Angle, 
fuppofe of^/o degrees, and to be well wrought, being 
made of Glafs free from Bubbles and Veins, with its fides 
not a little Convex or Concave as ufually happens but 
truly Plane,and its poUifh elaborate, as in working Optick- 

glafles 



[51] 

gkfles y and not fuch as is ufually wrought with Putty, 
whereby the edges of the Sand-holes being worn away, 
there are left all over the Glafs a numberlefs company of 
very little Convex polite rifings like Waves. The edges 
alfo of the Prifm and Lens fo far as they may make any 
irregular Refra6tion, muft be covered with a black Paper 
glewed on. And all the Light of the Sun's beam let into 
the Chamber which is ufelefs and unprofitable to the Ex- 
periment, ought to be intercepted with black Paper or other 
black Obftacles. For otherwife the ufelefs Light being 
refleded every way in the Chamber , will mix with the 
oblong Spedrum and help to difturb it. In trying thefe 
things fo much Diligence is not altogether neceflary, but 
it will promote the fuccefs of the Experiments, and by a 
very fcrupulous Examiner of things deferves to be applied. 
It's difficult to get glafs Prifms fit for this purpofe, and 
and therefore I ufed fometimes Prifmatick Vends made 
with pieces of broken Looking-glafles, and filled with rain 
Water. And to increafe the Refradion, I fometimes im- 
pregnated the Water ftrongly with Saccharum Saturni, 

PROP. v. Theor. IV. 

Homogeneal Light is refraBed regularly without any Dilatation 

f putting or Jhattering of the ^^ys , and the confufed Vtjton 

of OhjeBs feen through ^fraEling 'Bodies hy Heterogejieal 

Light arifes from the dtjferent ^efrangihtlity of federal forts 

of %y. J, 

TH E firft Part of this Propoficion has been already 
fufficiently proved in the fifth Experiment, and will 
further appear by the Experiments which follow. 

G 2 Exper. i 2. 



[52] 

Exper, 12. In the middle of a black Paper I made a 
round hole about a fifth or fixth part of an Inch in Dia- 
meter. Upon this Paper I caufed the Spectrum of Homo- 
geneal Light defcribed in the former Propofition , fo to 
fall, that fome part of the Light might pafs through the 
hole of the Paper. This tranfmitted part of the Light I 
refra^led with a Prifm placed behind the Paper, and let- 
ting this refraded Light fall perpendicularly upon a white 
Paper two or three Feet diftant from the Prifm, I found 
that the Spedrum formed on the Paper by this Light was 
not oblong, as when 'tis made (in the third Experiment) 
by Refracting the Sun's compound Light, but was (fo far 
as I could judge by my Eye) perfedly circular, the length 
being no greater than the breadth. Which fliews that this 
Light is refi:ad;ed regularly without any Dilatation of the 

Exper. 1 ;. In the Homogeneal Light I placed a^Circle 
of -^ of an Inch in Diameter, and in the Sun's unrefradted 
Heterogeneal white Light I placed another Paper Circle of 
the fame bignefs. And going from the Papers to thediftance 
of fome Feet, I viewed both Circles through a Prifm. The 
Circle illuminated by the Sun's Heterogeneal Light appear- 
ed very oblong as in the fourth Experiment , the length 
being many times greater than the breadth : but the other 
Circle illuminated with Homogeneal Light appeared Cir- 
cular and diftindly defined as when 'tis viewed with the 
naked Eye. Which proves the whole Propofition. 

Exper. 14. In the Homogeneal Light I placed Flies and 
fuch like Minute Objeds, and viewing them through a 
Prifm , I faw their Parts as diftindlly defined as if I had 
viewed them with the naked Eye. The fame Objeds pla- 
ced in the Sun's unrefraded Heterogeneal Light which was 
white I viewed alfo through a Prifm, and faw them moft 

confufedly 



[$3 3 

Gonfufedly defined, fo thatlcould not diftinguiflh their fmaU 
ler Parts from one another. I placed alfo the Letters of a 
fmall Print one while in the Homogeneal Light and then 
in the Heterogeneal, and viewing them through a Prifm, 
they appeared in the latter cafe fo confufed and indiftind: 
that I could not read them 5 but in the former they ap- 
peared fo diftindl that I could read readily, and thought 
I fav/ them: as diftind: as when I viewed them with my 
naked Eye. In both cafes I viewed the fame Objedls 
through the fame Prifm at the fame diftance from me and 
in the fame Situation. There was no difference but in the 
Light by which the Objects were illuminated , and which 
in one cafe was Simple and in the other Compound, and 
therefore the diftindl Vifion in the former cafe and confu- 
fed in the latter could arife from nothing elfe than from 
that difference of the Lights. Which proves the whole 
Propoficion. 

And in thefe three Experiments it is further very remar- 
kable, that the Colour of Homogeneal Light was never: 
changed by the Refradion.. 

PROP. Vr. Theor. V: 

The Sine of Incidence of eVery ^ay confidered apart ^ is to its SifWi 
of ^fraBion in a giyen ^l{atio. 

THAT every Ray confidered apart is conftant to 
it felf in fome certain degree of Refrangibility, is 
fufficiently manifeft out of what has been faid. Thofe 
Rays which in the firfl Refradion are at equal Incidences 
moll refraded, are alfo in the following Refractions at 
equal Incidences mofl refraded 5 and fo of the leafl Re- 
frangible , and the reft which have any mean degree of 

Refran-f 



[$4] 

Refran*gibility, as is manifeft by the 5th, 6th, 7th, 8th, 
and 9th Experiments. And thofe which the firft time at 
like Incidences are equally refraded, are again at like In- 
cidences equally and uniformly refraded, and that whe- 
ther they be refraded before they be feparated from one 
another as in the 5 th Experiment, or whether they be re- 
fraded apart, as in the i 2th, i ^th and 14th Experiments. 
The Refradion therefore of every Ray apart is regular, 
and what Rule that Refradion obferves we are now 
to fhew. 

The late Writers in Opticks teach, that the Sines of In- 
cidence are in a given Proportion to the Sines of Refra- 
dion, as was explained in the 5 th Axiom 5 and fome by 
Inftruments fitted for meafuring Refradions, or otherwife 
experimentally examining this Proportion, do acquaint us 
that they have found it accurate. But whilft they, not 
underftanding the different Refrangibility of feveral Rays, 
conceived them all to be refraded according to one and 
the fame Proportion, 'tis to be prefumed that they adapted 
their Meafures only to the middle of the refraded Light 5 
fo that from their Meafures we may conclude only that 
the Rays which have a mean degree of Refrangibility , 
that is thofe which when feparated from the reft appear 
green, are refraded according to a given Proportion of 
their Sines. And therefore we are now to fliew that the 
like given Proportions obtain in all the reft. That it 
fhould be fo is very reafonable. Nature being ever confor- 
mable to her felf : but an experimental Proof is defired. 
And fuch a Proof will be had if we can flhew that the 
Sines of Refradion of Rays differently Refrangible are 
one to another in a given Proportion when their Sines of 
Incidence are equal. For if the Sines of Refiradion of all 
the Rays are in given Proportions to the Sine of Refradion 

of 



M5] 

©f a Ray which has a mean degree of Refrangibility, and 
this Sine is in a given Proportion to the equal Sines of 
Incidence, thofe other Sines of Refradion will alfo be in 
given Proportions to the equal Sines of Incidence. Now 
when the Sines of Incidence are equal, it will appear by 
the following Experiment that the Sines of Refradion are 
in a given Proportion to one another. 

Exper. 15. The Sun flhining into a dark Chamber 
through a little round hole in the Window-fliut, let S re- ^5?* ^^' 
prefent his round white Image painted on the oppofite 
Wall by his dired Light, P T his oblong coloured Image 
made by refrading that Light with a Prifm placed at the 
Windowj and pt^ or ip it^ or ^p 3 f, hisoblong coloured 
Image made by refra6ling again the fame Light fideways 
with a fecond Prifm placed immediately after the firft in 
a crofs Pofition to it, as was explained in the fifth Experi- 
ment : that is to fay, pt when the Refraction of the fecond 
Prifm is fmall, ip it when its Refracftion is greater, and 
3^ 3/- when it is greateft. For fuch will be the diverfity J(- 
of the Refra6lions if the refra6ling Angle of the fecond 
Prifm be of various Magnitudes 3 fuppofe of fifteen or 
twenty degrees to make the Image p ?, of thirty or 
forty to make the Image ip 2 f, and of fixty to make 
the Image ip ^t. But for want of folid Glafs Prifms with 
Angles of convenient bignefles, there may be Veflels 
made of poliflhed Plates of Glafs cemented together in the 
form of Prifms and filled with Water. Thefc things being 
thus ordered, I obferved that all the folar Images or co- 
loured Spedrums P T, ^^, ip it^ 3^ 3^ did very nearly 
converge to the place S on which the dired: Light of the 
Sun fell and painted his white round Image when the 
Prifms were taken away. The Axis of the Spedrum PT, 
that is the Line drawn through the middle of it Parallel to 

its 



its Redilincar Sides, did when produced pafs exadly through 
the middle of that white round Image S. And when the 
Refradion of the fecond Prifm was equal to the Refradlion 
of the firft, the refradting Angles of them both being about 
^o degrees, the Axis ofthe Spedrum ip ^t made by that 
:Refra(5lion, did when produced pafs alfo through the mid- 
dle of the fame white round Image S. But when the Re- 
fraction of the fecond Prifm was lefs than that of the firft, 
the produced Axes of the Spedirums tp ox it zp made 
by that Refradion did cut the produced Axis of the Spe- 
<5lrum TP in the Points m and w, a little beyond the Cen- 
ter of that white round Image S. Whence the Proportion 
ofthe Line ^ f T to the Line ipV was a little greater than 
the Proportion of 2 f T to 2 /^P, and this Proportion a little 
greater than that of tT to j?P. Now when the Light of 
the Spc6lrumP T falls perpendicularly upon the Wall, thofe 
Lines 3 tT, 3-^ P, and 2 1 T, if P and ^T, ^P,are the Tan- 
gents of the Refrad:ions 3 and therefore by this Experiment 
the Proportions of the Tangents of the Refradiions are ob- 
tained, from whence the Proportions of the Sines being deriv- 
ed, they come out equal, fo far as by viewing the Sped:rums 
and ufing fome Mathematical reafoning I could Eftimate. 
For I did not make an Accurate Computation. So then 
the Propofition holds true in every Ray apart, fo far as ap- 
pears by Experiment. And that it is accurately true may 
j^-- be demonftrated upon this Suppofition, That bodies refraEi 
Light by aBing upon its (^ys in Lines Perpendicular to their 
Surfaces. But in order to this Demonftration , I muft di- 
ftinguifh the Motion of every Ray into two Motions, the 
one Perpendicular to the refra6ting Surface, the other Pa- 
rallel to it, and concerning the Perpendicular Motion lay 
down the following Propofition. 

If 



If any Motion or moving thing whatfoever be incident ^,'5 ii^V 
with any velocity on any broad and thin Space termina- O^.-^^^/^ 
ted on both fides by two Parallel Planes, and in its paflage ^-^^'^ 
through that fpace be urged perpendicularly towards the 
further Plane by any force which at given diftances from 
the Plane is of given quantities 3 the perpendicular Velo- 
city of that Motion or Thing, at its emerging out of that 
fpace, fliall be always equal to the Square Root of the 
Summ of the Square of the perpendicular Velocity of 
that Motion or Thing at its Incidence on that fpace 5 
and of the Square of the perpendicular Velocity which 
that Motion or Thing would have at its Emergence, if 
at its Incidence its perpendicular Velocity was infinitely 
little. 

And the fame Propofition holds true of any Motion or 
Thing perpendicularly retarded in its paflage through that 
fpace, if inftead of the Summ of the two Squares you take 
their difference. The Demonflration Mathematicians will ^h.Qi(iJ---P^7,.9nctk 
eafily find out, and therefore I fhall not trouble the Rea- ^^^--i9--'^(^7-^'r2 
der with it. 

Suppofe now that a Ray coming mofl obliquely in the/w-. u 
Line MC be refraded at C by the Plane RS into the Line 
CN, and if it be required to find the Line CE into which 
any other Ray AC fliall be refraded 5 let MC, AD, be 
the Sines of incidence of the two Rays, and NG, EF, their 
Sines of Rcfradion, and let the equal Motions of the In- 
cident Rays be reprefented by the equal Lines M C and 
AC, and the Motion MC being confidered as parallel to 
the refrading Plane, let the other Motion AC be diftin- 
guifhed into two Motions AD and DC, one of which 
AD is parallel, and the other DC perpendicular to the re- 
fracting Surface. In like manner, let the Motions of the 
emering Rays be diftinguifh'd into two, whereof the per- 

H pendicular 



perpendicular ones are -^ CG and ^p CF. And if the 

force of the refrading Plane begins to ad upon the Rays 
either in that Plane or at a certain diftance from it on the 
one fide, and ends at a- certain diftance from it^ on the 
other fide, and in all places between thofe two Limits ads 
upon the Rays in Lines perpendicular to that rafrading 
Plane, and the Adions upon the Rays at equal diftances 
from the refrading Plane Se equal, and at unequal ones ei- 
ther equal or unequal according to any rate whatever 3- 
that motion of the Ray which is Parallel to the refrading 
Plane will fufifer no alteration by that force 3 and that mo- 
tion which is perpendicular to it will be altered according 
to the rule of the foregoing Propofition. If therefore for 
the perpendicular Velocity of the emerging Ray CN you 

write 5^ CG as a-bove, then the perpendicular Velocity 



JD 



of any other emerging Ray CE which was ^ CF, will be 

A/fC n 

equal to the fquare Root of CD^ + -^^^ CGq, And 

by fquaring thefe equals, and adding to them the Equals 
AD^ and MC^ — CD^, and dividing the Summ.s by the 
Equals CVq+ EVq and CGq ^- NG^, you will have 

11^ equal to f|A Whence AD, the Sine of Incidence, 

is to EF the Sine of Refradion, as MC to NG, that isy 
in a given ratio. And this Demonftration being general, 
without determining what Light is, or by what kind of 
force it is refraded, or afluming any thing further than 
that the refrading Body ads upon the Rays in Lines per- 
pendicular to its Surface 5 I take it to be a very convincing 
Argument of the full Truth of this Propofition. 

60 



[$9] 

So th^n, if the ratio of the Sines of Incidence and Re- 
fraftion of any fort of Rays be found in any one Cafe, 'tis 
given in all Cafes 5 and this may be readily found by the 
Method in the following Propoiidon. 



PROP. VII. Theor. VI. 

The TerfeBmi of Tele/copes is impeded by the dijferent ^fraU" 
^ihiitty of the ^ys of Light, 

^ %^ H E imperfedion of Telefcopes is vulgarly attri- 
J^ buted to the fpherical Figures of the Glafles, and 
therefore Mathematicians have propounded to Figure them 
by the Conical Sediions. To ftiew that they are mifta- 
ken, I have inferted this Propofition^ the truth of which 
w^ill appear by the meafures of the Refra6lions of the feve- 
ral forts of Rays 3 and thefe meafures I thus determine. 

In the third experiment of the firft Book, where the re^ 
frat^ing Angle of the Prifm was 62' degrees, the half of 
that Angle 3 i deg. \ j min. is the Angle of Incidence of 
the Rays at their going out of the Glafs into the Air 3 and 
the Sine of this Angle is Jj^, the Radius being loooo. ^'^^7- r^ 
When the Axis of this Prifm was parallel to the tlorizon, 
and the Refraction of the Rays at their Incidence on this 
Prifm equal to that at their Emergence out of it, I obfervcd 
with a Quadrantthe Angle which the mean refrangible Rays 
(thatis, thofe which wentto the middle oftheSuns colour- 
ed Image ) made with the Horizon and by this Aagle and 
the Sun's altitude obferved at the fame time, I found the 
Angle which the emergent Rays contained with the incident 
to be 44 deg. and 40 min. and the half of this /Ingle ad- 
ded to the Angle of Incidence 3 i deg. 1 5 min. makes the 

H z Angle 



[do] 

Angle of Refradion,which is therefore 5 ; dcg. ^ 5 min. and 
its Sine 8047. Thefe are the Sines of Incidence and Rc-r 
fraaion of the mean refrangible Rays, and their proportion 
in round numbers is 20 to 3 1 . This Gl?Js was of a colouring- 
chnincT to green. The laft of the Prifms mentioned in the 
third Experiment was of clear white Glafs. Its refrading 
Angle 63 1 degrees. The Angle v/hich the emergent Rays 
contained, with the incident 45 deg. 50 min. The Sine of 
half the firft Angle 5262. The Sine of half the Summ. 
of the Angles 8157. And their proportion in round num- 
bers 20 to 31 as before. 

From the Length of the Image, which was about 9I or 
10 Inches, fubdud its Breadth, which was 2^ Inches, and 
the Remainder 7^ Inches would be the length of the Image 
were the Sun but a point, and therefore fubtends the An- 
gle which the moft and leaft refrangible Rays, when inci- 
dent on the Prifm in the fame Lines, do contain with one 
another after their Emergence. Whence this Angle is 
2 des. o.' 7' For the diftance between the Image and the 
Prifm where this Angle is made, was 1 8^ Feet, and at that 
diftance the Chord 7^ Inches fubtends an Angle of 2 deg.- 
o.' 7." Now half this Angle is the Angle which thefe e- 
mergent Rays contain with the emergent mean refrangible 
Rays, and a quarter thereof, that is 30. 2." m^^y be ac- 
counted the Angle which they would contain^'whidk the 
fame emergent mean refrangible Rays, were they co-inci- 
dent to them within the Glafs and fufFered no other Re- 
ff action then that at their Emergence. For if two equal 
Refra6tions the one at the incidence of the Rays on the 
Prifm the other at their Emergence, make half the Angle 
2 deg. 0.7. then one of thofe Refradions will make 
about a quarter of that Angle, and this quarter added to 

and 



ami fubduded from the Angle of Reftadion of the mean 
refrangible Rays, which was 5; deg. ^5', gives the An- 
gles or Refradion of the moft and leaft refrangible Rays 
54 deg. 5' 2", and 5^ deg. 4' 58", whofe Sines are 8099 
and 7995, the common Angle of Incidence being ^i deg. 
15' and its Sine 51885 and thefe Sines in the leaft round 
numbers are in proportion to one another as 78 and 77 
to 50. 

No\v if you fubdudl the common Sine of Incidence 50 ^ t^ 
from the Sines of Refraction 77 and 78, the remainders 
27 and 28 fliew that in fmall Refradlions the Refradion 
of the leaft refrangible Rays is to the Refradion of the moft 
refrangible ones as 27 to 28 very nearly, and that the dif- 
ference of the Refractions of the leaft refrangible and moft 
refrangible Rays is about the 27^th part of the whole Re- 
fraction of the mean refrangible Rays. 

Whence they that are skilled in Opticks will eafily un- ^ 
derftand, that the breadth of the leaft circular fpace into 
which Objecc-Glafles of Telefcopes can collect all forts of 
Parallel Rays, is about the 27jth part of half the aperture - 
of the Glafs, or 55 th part of the whole aperture 3 and 
that the Focus of the moft refrangible Rays is nearer to the 
Object-Glafs thanthe Focus of the leaft refrangible ones, by 
about the 27^'th part of the diftance between the Object- 
Glafs and the Focus of the mean refrangible ones. 

And if Rays of all forts,flowing from any one lucid point 
in the Axis of any convex Lens, be made by the Refraction 
of the Lens to converge to points not too remote from the 
Lens , the Focus of the moft refrangible Rays fliall be 
nearer to the Lens than the Focus of the leaft refrangible 
ones, by a diftance which is to the 27-~th part of the di- 
ftance of the Focus of the mean refrangible Rays from the 
Lens as the diftance between that Focus and the lucid 

point 



point from whence the Rays flow is to the diftance be- 
tween that lucid point and the Lens very neaily. 

"Now to examine whether the difference between the Re- 
fradlions which the moft refrangible and the leaft refran- 
gible Rays flowing from the fame point fiiffer in the Ob- 
jed-Glaffes of Telefcopes and fuch like Glaffes, be fo great 
as is here defcribed, I contrived the following Experi- 
ment. 

Exper. 1 6. The Lens which I ufed in the fecond and 
eighth Experiments, being placed fix Feet and an Inch dif- 
tant from any Objecfb, coUeded the Species of that Object 
by the mean refrangible Rays at the diftance of fix Feet 
and an Inch from the Lens on the other fide. And there- 
fore by the foregoing Rule it ought to colled: the Species of 
that Obje6l by the leaft refrangible Rays at the diftance of 
fix Feet and 3 - Inches from the Lens, and by the moft re- 
frangible ones at the diftance of five Feet and lof Inches 
from it : So that between the t\^ o Places where thefe leaft 
and moft refrangible Rays colledl the Species, there may 
be the diftance of about ^\ Inches. For by that Rule, as 
fix Feet and an Inch ( the diftance of the Lens from the 
lucid Object ) is to twelve Feet and two Inches ( the di- 
ftance of the lucid Object from the Focus of the mean re- 
frangible Rays) that is, as one is to two, fo is the 27j.th 
part of fix Feet and an Inch (the diftance between the Lens 
and the fame Focus ) to the diftance between the Focus of 
the moft refrangible Rays and the Focus of the leaft re- 
frangible ones, which is therefore 5 ^ Inches, that is very 
nearly 5 : Inches. Now to know whether this meafure 
was true, I repeated the fecond and eighth Experiment of 
this Book with coloured Light, which Vv^as lefs compound- 
ed than that I there made ufe of : For I now feparat:ed the 

hetero- 



h eterogeneous Rays from one another by Ae Method I de- 
fc ribed in the i ith Experiment, fo as to make a coloured 
Spedrum about twelve or fifteen times longer than broad. 
This Spedrum I caft on a printed book, and placing the 
above-mentioned Lens at the diftance of fix Feet and an 
Inch from this Spedrum to colled the Species of the illu- 
minated Letters at the fame diftance on the other fide, I 
found that the Species of the Letters illuminated with Blue 
were nearer to the Lens than thofe illuminated with deep 
Red by about three Inches or three and a quarter : but the 
Species of the Letters illuminated with Indigo and Violet 
appeared fo confufed and indiftind, that I could not read 
then-^ : Whereupon viewing the Prifm, I found it was full 
of Veins running from one end of the Glafs to the other ^ 
fo that the Refradian could not be regular. I took ano- 
ther Prifm therefore which was free from Veins, and in- 
ftead of the Letters I ufed two or three Parallel black Lines 
a little broader than the ftroakes of the Letters, and caft- 
ing the Colours upon thefe Lines in fuch manner that the 
Lines ran along the Colours from one end of the Spedum 
to the other, I found that the Focus where the Indigo, or 
confine of this colour and Violet caft the Species of the 
black Lines moft diftindly,to be about 4 Inches or 4^ nea^-^ sl^ //?/v*/ 1 
er to the Lens than the Focus where the deqt^ Red^caff^^^*-^!*^^^. j 
the Species of the fame black Lines moft diftindly. ^ I 

The violet was fo faint and dark, that I could not 
difcern the Species of the Lines diftinctly by that Co- 
lour 3 and therefore confidering that the Prifm was made 
©f a dark coloured Glafs inchning to Green, I took another 
Pifm of clear white Glafs 3 but the Spedlrum of Colours 
which this Prifm made had long white Streams of faint 
Light fliooting out from both ends of the Colours, which 
made me conclude that fomething was amifs 3 and view- 



in 



f 



iiig the Prifm, 1 found two or three little Bubbles in the 
Glafs which refraded the Light irregularly. Wherefore I 
covered that part of the Glafs with black Paper, and let- 
ting the Light pafs through another part of it which was 
free from fuch Rubles, the Spedlrum of Colours became 
free from thofe irregular Streams of Light, and was now 
fuch as I defired. But ftill I found the Violet fo dark and 
faint, that I could fcarce fee thrfp^cies of the Lines by the 
Violet, and not at all by the d^^St part of it, which was 
next the end of the Spedrum. I fufpeded therefore that 
this faint and dark Colour might be allayed by that fcat- 
tering Light which was refracted, and reflected irregularly 
partly by fome very fmall Bubbles in the Glafles and 
partly by the inequalities of their PoliiGb: which Light, 
tho' it was but little, yet it being of a White Colour, 
might fuffice to affedl the Senfe fo ftrongly as to difturb 
the Phenomena of that weak and dark Colour the Violet, 
and therefore I tried, as in the nth, i5th5Ki4th Experi- 
ments, whether the Light of this Colour did not confift of 
a fenfible mixture of heterogeneous Rays, but found it did 
not. Nor did the Refractions caufe any other fenfible 
Colour than Violet to emerge out of this Light, as they 
would have done out of White Light, and by con- 
fequence out of this Violet Light had it been fenfi- 
bly compounded with White Light. And therefore I con- 
cluded, that the reafon why I could not fee the Species of 
the Lines diflinClly by this Colour, was only the darknefs 
of this Colour and Thinnefs of its Light, and its dif- 
tance from the Axis of the Lens 5 I divided therefore thofe 
Parallel Black Lines into equal Parts, by which I might 
readily know the diftances of the Colours in the Spedrum 
from one another, and noted the diftances of the Lens 
from the Foci of fuch Colours as caft the Species of the 

Lines 



Lines diftin^lly, and then confidered whether the diffe- 
rence of thofe diftances bear fuch proportion to 5 '-Inches, 
the greateft difference of the diftances which the Foci of 
the deepeft Red and Violet ought to have from the Lens, 
as the diftance of the obferved Colours from one another 
in the Spedrum bear to the like diftance of the deepeft Red 
and Violet meafured in the redlilinear fides of the Speifl- 
rum, that is, to the length of thofe fides or excefs oF the 
length of the Spectrum above its breadth. And my Ob- 
fervations were as follows. n^jy ^^.^r^u^i-Al^^'ifsa^. 

When I obferved and compared the deepeft lenfibleRed, 
and thc^Colour in the confine of Green and Blue, which 
at that^''i:cd:ilinear fides of the Spectrum was diftant from it 
half the length of thofe fides, the Focus where the confine 
of Green and Blue caft the Species of the Lines diftindtly 
on the Paper, was nearer to the Lens then the Focus where 
the Red caft thofe Lines di6lin6lly on it by about 2 - or 
2 ^ Inches. For fontetimes the Meafures were a little grea- 
ter, fomctimes a little lefs, but feldom varied from one 
another above \ of an Inch. For it was very difficult to 
define the Places of the Foci, without fome little Errors. 
Now if the Colours diftant half the length of the Image, 
( meafured at its redtilinear fides ) give i ^ or 2 | difference 
of the diftances of their Foci from the Lens, then the Co- 
lours diftant the whole length ought to give 5 or 5-' Inches 
difference of thofe diftances. 

But here it's to be noted, that I could not fee the Red 
to the full End of the Spedrum, but only to the Center 
of the Semicircle which bounded that End, or a little far- 
ther 5. and therefore I compared this Red not with that Co- 
lour which was exadlly in the middle of the Specftrum, or 
confine of Green and Blue, but with that which verged a 
little more to the Blue than to the Green ; And as I reck- 

I 



oned the whole length of the Colours not to be the whole 
length of the Spectrum, but the length of its redlilinear 
fideSj fo completing theSemicirlar Ends into Circles, when 
cither of the obfcrved Colours fell within thofe Circles, I 
meafured the diftance of that Colour from the End of the 
Spedrum, and fubduding half the diftance from the mea- 
fured diftance of the Colours, I took the remainder for 
their correded diftance 3 and in thefe Obfervations fee 
down this correded diftance for the difference of their di« 
ftances from the Lens. For as the length of the redlilinear 
fides of the Spedrum would be the whole length of all the 
Colours, were the Circles of which ( as we (hewed ) that 
Spedrum confifts contra6ted and reduced to Phyfical 
Points, fo in that Cafe this corredlcd diftance would be the 
real diftance of the obferved Colours. 

When therefore I further obferved the deepeftfenfible Red^ 
and that Blue whofe correded diftance from it was ^ parts 
of the length of the redilinear fides of the SpecStrum, the 
difference of the diftances of their Foci from the Lens was 
about ^- Inches, and as 7 to 1 2 fo is 3 -^ to 5 ^. 

When I obferved the deepeft fenfible Red, and that Indi- 
go whofe correded diftance was -^ or ^ of the length of the 
redilinear fides of the Spedlrum, the difference of the di- 
ftances of their Foci from the Lens, was about 3 "^ Inches, 
and as 2 to 3 fo is 3 ^to 5I;. 

When I obferved the deepeft fenfible Red, and that deep 
Indigo whofe correded diftance from one another was ^ or 
'^- of the length of the redilinear fides of the Spedum, the 
difference of the diftances of their Foci from the Lens was 
about 4 Inches 5 and as 3 to 4 fo is 4 to 5 \, 

When I obferved the deepeft fenfible Red, and that part 
of the Violet next the Indigo whofe correded diftance from 
the Red was ^^ or ^ of the length of the redilmear fides of 

the 






the SpeArum, the difference of the diftances of their Foci 
from the Lens was about 4^ Inches 3 and as 5 to 6, fo is 
47 to 57. For fometimes when the Lens was advantagi- 
oufly placed, fo that its Axis relpeded the Blue, and ail 
things elfe were well ordered, and the Sun flhone clear, and 
I held my Eye very near to the Paper on which the Lens 
caft the Species of the Lines, I could fee pretty diftinctly 
the Species of thofe Lines by that part of the Violet which 
was next the Indigo 3 and fometimes I could fee them by 
above half the Violet. For in making thefe Experiments 
I had obferved, that the Species of thofe Colours only ap- 
peared diffinct which were in or near the Axis of the Lens : 
So that if the Blue or Indigo were in the Axis, I could fee 
their Species diftinctly 5 and then the Red appeared much 
lefs diftinct than before. Wherefore I contrived to make 
the Spectrum of Colours fliorter than before, fo that both 
its Ends might be nearer to the Axis of the Lens. And 
now its length was about li Inches and breadth about -or 
i of an Inch. Alfo inftead of the black Lines on which the 
Spectrum was caft, I made one black Line broader than 
thofe, that I might fee its Species more eafily 3 and this 
Line I divided by fliort crofs Lines into equal Parts, for 
meafuringthe diftances of the obferved Colours. And now 
I could fometimes fee the Species of this Line with its divi- 
lions almoft as far as the Center^ of the Semicircular Violet 
End of the Spectrum, and made thefe further Obfervations. 
When I obferved the deepeft feofible Red, and that part 
of the Violet whofe correded diftance frcni it v/as about 
^ Parts of the re6tilinear fides of the Spedrum the difference 
of the diftances of the Foci of thofe Colours from the Lens, 
was one time 4-% another time 4^, anothertime 41^ Inches, 
and as 8 to 9, fo are 4^, 4-;, 4I, to 5 -;, 5^^ 5IJ refpedively. 

I 2 When 



[68] 

When I obferved the deepeft fenfible Red, and deeped 
fenfible Violet, (the corrected diftance of which Colours 
when all things were orderedto the bed advantage, andthe 
Sun flione very clear, was about ^ or ^ parts of the length 
of the rectilinear fides of the coloured Spectrum, ) I found 
the difference of the diftances of their Foci from the Lens 
fometimes 4-' fometimes 5^, and for the moft part 5 Inches 
or thereabouts : and as 11 to 1 2 or 15 to |6, fo is five 
Inches to 5 ^- or 5 i Inches. 

And by this progreffion of Experiments I fatisfied my 
felf, that had the light at the very Ends of the Spectrum been 
ftrong enough to make the Species of the black Lines ap- 
pear plainly on the Paper, the Focus of the dcepeft Vio- 
let would have been found nearer to the Lens, than the Fo- 
cus of the deepeft Red, by about y- Inches at leaft. And 
this is a further Evidence, that the Sines of Incidence and 
Refraction of the feveral forts of Rays, hold the fame pro- 
portion to one another in the fmalleft Refractions which 
they do in the greatefl:. 

My progrefs in making this nice and troublefome Expe- 
riment I have fet down more at large, that they that fhall 
try it after me may be aware of the Circumfpe<5tion re- 
quifite to make it fucceed well. And if they cannot make 
it fucceed fo well as I did, they may notwithftanding col- 
lect by the Proportion of the diftance of the Colours in the 
Spedtrum, to the difference of the diftances of their Foci 
from the Lens, what would be the fucccfs in the more di- 
ftant Colours by a better Trial. And yet if they ufe a 
broader Lens than I did, and fix it to a long ftreight Staff 
by means of which it may be readily and truly directed to 
the Colour whofe Focus is defired, I queftion not but the 
Experiment will fucceed better with th^m than it did with 
me. Fox I directed the Axis as nearly as I could to the 

middle 



L^9l 

middle of the Colours, and then the faint Ends of the 
Spedrum being remote from the Axis, caft their Species lefs 
diftin(5lly on the Paper than they would have done had the 
Axis been fucceffively diredred to them. 

Now by what has been faid its certain, that the Rays 
which differ in refrangibility do not converge to the fame 
Focus, but if they flow from a lucid point, as far from 
the Lens on one fide as their Foci are one the other, the 
Focus of the moft refrangible Rays fliall be nearer to the 
Lens than that of the leaft refrangible, by above the four- 
teenth part of the whole diftance: and if they flow from a lu- 
cid point, fo very remote from the Lens that before their 
Incidence they may be accounted Parallel, the Focus of the 
moil refrangible Rays fhall be nearer to the Lens than the 
Focus of the leafl: refrangible, by about the 27th or 28th part 
of their whole diflance from it. And the Diameter of the 
Circle in the middle fpace between thofe two Foci which 
they illuminate when they fall there on any Plane, perpen- 
dicular to the Axis (which Circle is the leafl: into which 
they can all be gathered) is about the 55th part of the Dia- 
meter of the aperture of the Glafs. So that 'tis a wonder 
that Telefcopes reprefent Objects fo diflrindt as they do. But 
were all the Rays of Light equally refrangible, the Error 
arifing only from the fphericalnefs of the Figures of Glafles 
would be many hundred times lefs. For if-the Objed- 
Glafs of a Telefcope be Plano-convex, and the Plane fide 
be turned towards the Objed, and the Diameter of the 
Sphere whereof this Glafs is a fegment,be called D, and the 
Semidiameter of the aperture of the Glafs be called S, and 
the Sine of Incidence out of Glafs into Air, be to the Sine of 
Refradion as I to R: the Rays which come Parallel to the 
Axis of the Glafs, fliall in the Place where the Image of the 
Object is mofl: diftindly made, be fcattered all over a little 

Circle 



[7°] 

Circle whofe Diameter is j ^ ^ — ^^ very nearly, as I ga- 
ther by computing the Errors of the Rays by the method 
of infinite Series, and rejeding the Terms whofe quanti- 
ticies are inconfiderable. As for inftance, if the Sine of In- 
cidence I, be to the Sine of Refradion R, as 20 to ^ i, and 
if D the Diameter of the Sphere to which the Convex fide 
of the Glafs is ground, be 100 Feet or 1200 Inches, and 
S the Semidiameter of the aperture be two Inches, the 

Diameter of the little Cirde ( that is j^D^Ii/. ) ^^'^ ^^ 



21 •>< 



20 >^ 1200 ■?< 120Q ^ 3 

Diameter of the little Circle through which thefe Rays are 
Scattered by unequal refrangibility, will be about the 55th 
part of the aperture of the Objed-Glafs which here is four 
Inches. And therefore the Error arifing from the fpherical 
Figure of the Glafs, is to the Error anfing from the diffe- 
rent Refrangibility of the Rays, as j^^ to ^ that is as i 
to 8151 : and therefore being in Comparifon fo very little, 
deferves not to be confidered. 
# But you will fay, if the Errors caufed by the different re- 
frangibility be fo very great, how comes it to pafs that Ob- 
jeds appear through Telefcopes fo diflind as they do ? I an- 
fwer, 'tis becaufe the erring Rays are not fcattered uniform- 
ly over all that circular fpace, but collected infinitely more 
denfely in the Center than in any other part of the Circle, 
and in the way from the Center to the Circumference grow 
continually rarer and rarer, fo as at the Circumference to 
become infinitely rare 3 and by reafon of their rarity are 
-. not fl:rong enough to bevifible, unlefs in the Center and ve- 

^S* '^'^' j.y near it. Let AD E reprefent one of thofe Circles de- 
fcribed vv^ith the Center C and Semidiameter AC, and let 
BFG be a fmaller Circle concentric to the former, cutting 

with 



I 



[71] 

With its Circumference the Diameter AC in B^ and b^fect 
AC in N, and by my reckoning the denfity of the Light 
in any place B will be to its denfity inN, as AB to BC3 
and the whole Light within the leffer Circle BFG, will be 
to the whole Light within the greater AED, as the Excefs of 
the Square of AC above the Square of AB, is tojthe Square 
of AC. As if BC be the fifth part of AC, the Light will be 
four times denfer in Bthan in N, and the whole Lightwith- 
in the lefs Circle,will be to the whole Light within the grea- 
ter, as nine to twenty five. Whence it's evident that the 
Light within the lefs Circle, muflftrike the fenfe much more 
ftrongly, than that faint and dilated light round about be- 
tween it and the Circumference of the greater. 

But its further to be noted, that the moft luminous of , e , ^^^ 
the prifmatick Colours are the Yellow and Orange. ^\\t{zW. JLr^-,u2^(SZe^y^H 
affea the Senfes more ftrongly than all the reft" together, and -^-^^-f^"^.^"'^^^ 
next to thefe in ftrength are the Red and Green. The Blue 
compared with thefe is a faint and dark Colour, and the In- 
digo and Violet are much darker and fainter, fo that thefe 
compared with the ftronger Colours are little to be regard- 
ed. The Images of Objedls are therefore to be placed, not 
in the Focus of the mean refrangible Rays which are in the 
confine of Green and Blue, but in the Focus of thofe Rays 
which are in the middle of the Orange and Yellow 3 there 
where the Colour is moft luminous and fulgent, that is in 
the brighteft Yellow, that Yellow which inclines more to 
Orange than to Green. And by the Refradlion of thefe 
Rays ( whofe Sines of Incidence and Refradlion in Glafs 
are as 17 and 11) the Refradion of Glafs and Cryftal for 
optical ufes is to be meafured. Let us therefore place the 
Image of the Objed in the Focus of thefe Rays, and all the 
Yellov/ and Orange will fall within a Circle, whofe Dia- 
meter is about the zjoth part of the Diameter of the aper- 
ture 



[72] 

ture of the Giafs. And if you add the brighter half of the 
Red, ( that half which is next the Orange, and the brighter 
half of the Green, ( that half which is next the Yellow, ) a- 
bout three fifth parts of the Light of thefe two Colours will 
fall within the fame Circle,and two fifth parts will fall with- 
out it round about 5 and that which falls without will be 
ipread through almoft as much more fpace as that which 
falls within, and fo in the grofs be almoft three times ra- 
rer. Of the other half of the Red and Green, ( that is of 
the deep dark Red and Willow Green ) about one quarter 
will fall within this Circle, and three quarters without, and 
that which falls without will be fpread through about four 
or five times more fpace than that which fall$within5 and fo 
in the grofs be rarer, and if compared with the whole Light 
within it, will be about 25 times rarer than all that taken in 
the grofs 3 or rather more than ^ o or 40 times rarer, be- 
caufe the deep red in the end of the Spe6trum of Colours 
made by a Prifm is very thin and rare, and the Willow Green 
is fomething rarer than the Orange and Yellow. The Light 
of thefe Colours therefore b£ing fo very much rarer than that 
within the Circle, will fcarce affedt the Senfe efpecially fince 
the deep Red and Willow Green of this Light, are much 
darker Colours then the reft. And for the fame reafon the 
Blue and Violet being much darker Colours than thefe, and 
much more rarified, may be neglected. For the denfe and 
bright Light of the Circle, will obfcure the rare and weak 
Light of thefe dark Colours round about it, and render them 
almoft infenfible. The fenfible Image of a lucid point is 
therefore fcarce broader than a Circle Vv^hofe Diameter is 
the 250th part of the diameter of the aperture of the Object 
Glafs of a good Telefcope, or not much broader, if you 
except a faint and dark mifty light round about it, which 
a Spedator will fcarce regard. And therefore in a Telefcope 

whofc 



[73] 

whofe aperture is four Inches, and length an hundrec! Feety 
it exceeds not 2 '45", or 3". And in a Telcfcope whofe 
aperture is two Inches, and length 20 or 30 Feet, it may 
be 5 ' or 6" and fcarce above. And this Anfwers well to 
Experience : For fome Aflronomers have found the Dia- 
meters of the fixt Stars, in Telefcopes of between twenty 
and fixty Feet in length, to be about 4" or 5" or at mofl: 
^ in Diameter. But if the Eye-Glafs be tindled faintly 
with the fmoke of a Lamp or Torch, to obfcure the Light 
of the Star, the fiinter Light in the circumference of the 
Scar ceafes to be vifible, and the Star (if the Glafs be fuffici- 
ently foiled with fmoke) appears fomething more like a Ma- 
thematical Point. And for the fame reafon, the enormous 
part of the Light in the Circumference of every lucid Point 
ought to be lefs difcernable in fliorter Telefcopes than in 
longer, becaufe the fliorter tranfmit lefs Light to the Eye. ^^S^V^^w ^^*H'' 
Now if we fuppofe the fenfible Image of a lucid poinr/^;/* p^/^r^ tT^^!^ 
to be even 250 times narrower than the aperture of thei^^^^'l^f^'J 
Glafs: yet were it not for the different refrangibility of ^z^^f/^^ PJih'^\ 
Rays, its breadth in an 100 Foot Telefcope whofe aperture.r^'^/.^^'^^v£|, 
is 4 Inches would be but ,-^;^ parts of an Inch, as is ma-^^f^t fq^^j 
nifcfl by the foregoing Computation. And therefore '^^^^xJ£l'^C^'C^ 



this Cafe the greatefl: Errors arifing from the fpherical Figure •^"^*||^ <^i^^^v^^-mU) 

of the Glafs, would be to the greatefl fenfible Errors ari-«''^i^^'^^/2/JJ^i 

fing from the different refrangibility of the Rays as ■^^^^'^f^'^ 

to ^^ at mofl, that is only as i to 1826. And this fufli- 

ciently fliews that it is not the fpherical Figures of GlafTes 

but the different refrangibility of the Rays which hinders the 

perfection of Telefcopes. 

There is another Argument by which it may appear that 
the different refrangibility of Rays, is the true Caufe of the 
impe^fedion of Telefcopes. For the Errors of the Rays 
arifing from the fpherical Figures of Objed- GlafTes, are as 

K the 




972 /^im. 



I 



[74- 1 

the Cubes of the apertures of the Objeft-Glafles^and thence 
to make Telefcopes of various lengths, magnify with equal 
diftindnefs, the apertures of the Objed-GlafTes, and the 
Charges or magnifying Powers, ought to be as the Cubes of 
the fquare Roots of their lengths 5 which doth not anfwer 
to Experience. But the errors of the Rays arifing from, 
the different refrangibiHty, are as the apertures of the Ob- 
jed-»Glaffes, and thence to make Telefcopes of various 
lengths, magnify with equal diftindnefs, their apertures and 
charges ought to be as the fquare Roots of their lengths 5 
and this anfwcrs to experience as is well known. For in- 
ftance, a Telefcope of 64 Feet in length, with an aperture 
of 1' Inches, magnifies about i 20 times, with as much dif- 
tindnefs as one of a Foot in length, with ^ of an Inch aper- 
ture, magnifies 1 5 times. 

Now were it not for this different refrangibility of Rays, 
Telefcopes might be brought to a greater Perfedion than 
we have yet defcribed, by compofing the Objed^Glafs of I 
two Glafles with Water between them. Let ADFC repre- I 
fig, iS.f^nt the Gbjed-Gla(s compofed of two Glaffes ABED and | 
and BEFC, alike convex on the outfides AGD and CHF, 
and alike concave on the infides BME, BNE, with Water 
in the concavity BMEN. Let the Sine of Incidence out of 
Glafs into Air be as I to R and out of Water into Air as K 
to R, and by confequence out of Glafs into Water, as I to 
K : and let the Diameter of the Sphere to which the convex 
fides AGD and CHF are ground be D, and the Diameter 
of the Sphere to which the concave fides BME and BNE 
are ground be to D, as the Cube Root of KK— KI to the 
Cube Root of RK— RI: and the Refradions on the con- 
cave fides of the Glaffes, will very much corred the Errors 
of the Refradions on the convex fides, fo far as they arife 
from the fphericalnefs of the Figure. And by this means 

might 



I 



C 75 ] 

might Telefcopes be brought to fufficientperfeaion, wereit 
not forthediflferentreftangibiUty offeveralforsofRays. But 
by reafon of this difFerent refrangibility, I do not yet fee any 
other means of improving Telefcopes by Refractions alone 
than that of increafing their lengths, for which end the late y 
contrivance of Hugmms feems well accommodated. For 
very long Tubes are cumberfome, and fcarce to be readily 
managed, and by reafon of their length are very apt to 
bend, and fhake by bending fo as to caufe a continual 
trembling in the Objedls, whereby it becomes difficult to 
fee them diftindlly : whereas by his contrivance the Glafles 
are readily manageable, and the Obje6t-Glafs being fixt up- 
on a ftrong upright Pole becomes more fteddy. 

Seeing therefore the improvement of Telefcopes of given 
lengths by Refra<5lions is delperate ^ I contrived heretofore a 
Perlpeiflive by reflexion, ufing inftead of an Objed: Glafs 
a concave Metal. The diameter of the Sphere to which 
the Metal was ground concave was about 2 5 Englifh Inches, 
and by confequence the length of the Inftrument about fix 
Inches and a quarter. The Eye-Glafs was plano-convex, 
and the Diameter of the Sphere to which the convex fide was 
ground was about i of an Inch, or a little lefs, and by con- 
fequence it magmfied between \ o and 40 times. By ano- 
ther way of meafuring I found that it magnified about 
\ 5 times. The Concave Metal bore an aperture of an Inch 
and a third part 3 but the aperture was limited not by an 
opake Circle, covering the Limb of the Metal round about, 
but by an opake circle placed between the Eye-Glafs and the 
Eye, and perforated in the middle with a little round hole 
for the Rays to pafs through to the Eye. For this Circle 
by being placed here, ftopt much of the erroneous Light, 
which otherwife would have difturbed the Vifion. By com- 
paring it with a pretty good Perfpedive of four Feet iti 

K 2 length. 



length, made with a concave Eye-Glafs, I could read at a 
greater diftance with my own Inftrument than with the 
Glafs. Yet Objeds appeared much darker in it than in the 
Glafs, and that partly becaufe more Light was loft by re- 
flexion in the Metal, then by refradion in the Glafs, and 
partly becaufe my Inftrument was overcharged. Had it 
magnified but ^oor 2 5 times it would have made the Object 
appear more brisk and pleafant. Two of thefelmade about 
1 6 Years ago, and have one of them ftill by me by which 
I can prove the truth of what I write. Yet it is not fo good 
as at thefirft. For the concave has been divers times tar- 
niflied and cleared again, by rubbing it with very foft Lea- 
ther. When I made thefe, an Artift in honion undertook 
to imitate it 5 but ufing another way of poliflhing them 
than I did, he fell much fliort of what I had attained to 
as r afterwards underftood by difcourfing the under- Work- 
man he had imployed. The Polifli I ufed was on this man- 
ner. I had two round Copper Plates each fix Inches in 
Diameter, the one convex the other concave, ground ve- 
ry true to one another. On the convex I ground the Ob- 
3e(5l-Metal or concave which v/as to be polifh'd, till it had 
taken the Figure of the convex and was ready for a Polidi. 
Then I pitched over the convex very thinly, by dropping 
melted pitch upon it and warming it to keep the pitch 
foft, whilft I ground it with the concave Copper wetted to 
make it fpread evenly all over the convex. Thus by work- 
ing it well I made it as thin as a Groat, and after the con- 
vex was cold I ground it again to give it as true a Figure as 
I could. Then I took Putty which I had made very fine 
by waflhing it from all its grofler Particles, and laying a lit- 
tle of this upon the pitch, I ground it upon the Pitch with 
the concave Copper till it had done making a noife^ and 
then upon the Pitch I ground the Objeft-Metal with a brisk 

Motion 



"> 



[77] 

Motion, for about two or three Minutes of time, leaning 
hard upon it. Then I put frefli Putty upon the Pitch and 
ground it again till it had done making a noife, and after- 
wards ground the Objed Metal upon it as before. And 
this Work I repeated till the Metal was polifhed, grinding 
it the laft time with all my ftrength for a good while toge- 
ther, and frequently breathing upon the Pitch to keep it 
moift without laying on any more freflh Putty. The Ob- 
jedi'Metal was two Inches broad and about one third part 
of an Inch thick, to keep it from bending. I had two of 
thefe Metals, and when I had poliflied them both I tried 
which was beft, and ground the other again to fee if I could 
make it better than that which I kept. And thus by many 
Trials I learnt the way of polifliing, till I made thofe two 
refleding Pelpe6lives I fpake of above. For this Art of 
polifliing will be better learnt by repeated Practice than by 
my defcription. Before I ground the ObjeA Metal on the 
Pitch, I always ground the Putty on it with the concave 
Copper till it had done making a noife, becaufe if the Par- 
ticles of the Putty were not by this means made to ftick 
faft in the Pitch, they would by rolling up and down grate 
and fret the Objed Metal and fill it full of little holes. 

But becaufe Metal is more difficult to polifli than Glafs 
and is afterwards very apt to be fpoiled by tarnifliing, and 
reflects not fo much Light as Glafs quick^filvered over does: 
I would propound toufeinfteadof theMetal, a Glafs ground 
concave on the forefide, and as much convex on the back- 
fide, and quick-filvered over on the convex fide. The Glafs 
muft be every where of the fame thicknefs exadly. Other- 
wife it will make Objeds look coloured and indiftind. By 
fuch a Glafs I tried about five or fix Years ago to make 
a refleding Telefcope of four Feet in length to magnify a- 
bout 150 times, and I fatisfied my felf that there wants no- 
thing 



[78] 

thing but a good Attift to bring the defign to Perfe£i:iOft. 
For the Glafs being wrought by one of our London Artifts 
after fuch a manner as they grind Glaffes for Telefcopes, 
tho it feemed as well wrought as the Objedl Glafles ufe to 
be, yet when it was quick- filvered, the reflexion difcovered 
innumerable Inequalities all over the Glafs. And by reafon 
of thefe Inequalities, Obje6ls appeared indiftindl in this In- 
ftrument. For the Errors of refleded Rays caufed by any 
Inequality of the Glafs, are about fix times greater than the 
Errors of refraded Rays caufed by the like InequaUties. Yet 
by this Experiment I fatisfied my felf that the reflexion on 
the concave fide of the Glafs, which I feared would difliurb 
the vifion,didno fenfible prejudice to it, and by confequencc 
that nothing is wanting to perfe6t thefe Telefcopes, but 
good Workmen who can grind and polifli Glafles truly (phe- 1 
rical. An Obje^t-Glafs or a fourteen Foot Telefcope, made 
by one of our London Artificers, I once mended confidera- 
bly, by grinding it on Pitch with Putty, and leaning ve- 
ry eafily on it in the grinding, lefl: the Putty fliould fcratch 
it. Whether this way may not do well enough for polifli- 
ing thefe refleding Glafles, I have not yet tried. But he 
that fliall try either this or any other way of polifliing which 
he may think better, may do well to make his Glafles rea- 
dy for polifliing by grinding them without that violence, 
wherewith our London Workmen prefs their Glafles in grind- 
ing. For by fuch violent preflure, Glafles are apt to bend 
a little in the grinding, and fuch bending will certainly fpoil 
their Figure. To recommend therefore the confideration 
of thefe refleding Glafles, to fuch Artifts as are curious in 
figuring <jlafles, I fliall defcribe this Optical Inftrument in 
the following Propofition. 



PROP. 



[79] 
VROV. VII. Prob. II. 

To p?orlen Tele/copes. 

TET ABDC reprefent a Glafs fpherically concave on p;^^ ^^ 
^ the forefide AB, and as much convex on the back- 
fide CD, fo that it be every where of an equal thicknefs. Let 
It not be thicker on one fide than on the other, lefl: it make 
Objeds appear coloured and indiftind:, and let it be very 
truly wrought and cjuick-filveredoveron the backfide ^ and 
fet in the Tube VXYZ which muft be very black within. 
Let EFG reprefent a Prifm of Glafs or Cryftal placed near 
the other end of the Tube, in the middle of it, by means of 
a handle of Brals or Iron FGK, to the end of which made 
flat it is cemented. Let this Prifm be redangular at E, and 
let the other two Angles at F and G be accurately equal to 
each other, and by confequence equal to half right ones, and 
let the plane fides FE and GE be fquare, and by confe- 
quence the third fideFG a re(5tangular parallelogram, whofe 
length is to its breath in a fubduplicate proportion of two 
to one. Let it be fo placed in the Tube, that the Axis of 
the Speculum may pafs through the middle of the fquare 
fide EF perpendicularly, and by confequence through the 
middle of the fide F G at an Angle of 45 degrees, and let the 
fide EF be turned towards the Speculum, and the diftance 
of this Prifm from the Speculum be fuch that the Raysof the 
light PQ, RS, dec. which are incident upon the Speculum in 
Lines Parallel to the Axis thereof, may enter the Prifm at 
the fide EF, and be reiecSed by the fide F G, and thence 
go out of it through the fide GE, to the point T which 
muft be the common Focus of the Speculnm ABDC, and of 
a Plano-convex Eye-Glafs H, through which thofe Rays 
muft pafs to the Eye. And let the Rays at their coming 

out 



[8o] 

out of the Glafs pafs through a fmall round hole, or aper- 
ture made in a little Plate of Lead, Brafs, or Silver, where- 
with the Glafs is to be covered, which hole muft be no 
bigger than is neceflary for light enough to pafs through. 
For fo it will render the Object diftind, the Plate in which 
^tis made intercepting all the erroneous part of the Light 
which comes from the Verges of the Speculum AB. Such 
an Inftrument well made if it be 6 Foot long, ( reckoning 
the length from the Speculum to the Prifm, and thence to 
the Focus T ) will bear an aperture of 6 Inches at the Spe- 
culum, and magnify between two and three hundred times. 
But the hole H here limits the aperture with more advan- 
tage, then if the aperture was placed at the Speculum. If 
che Inftrument be made longer or fliorter, the aperture muft 
be in proportion as the Cube of the fquare Root of the 
length, and the magnifying as the aperture. But its con- 
venient that the Speculum be an Inch or two broader than 
the aperture at the leaft, and that the Glafs of the Speculum 
be thick, that it bend not in the working. The Prifm EFG 
muft be no bigger than is neceflary, and its back fide FG 
muft not be quick-filvered over. For without quick-filver 
it will refled all the Light incident on it from the Speculum. 
In this Inftrument the Objedl will be inverted, but may 
be eredted by making the fquare fides EF and EG of the 
Prifm EFG not plane but fpherically convex, that the Rays 
may crofs as well before they come at it as afterwards be- 
tween it and the Eye- Glafs. If it be defired that the Inftru- 
ment bear a larger aperture, that may be alfo done by com- 
pofing the Speculum of two Glaffes with Water between 
•them. ^^'^ V " ^ /^^?^ «/ ^y/^ ^v/f./^;. W ^p^ -^-z ^c^j'-^^ j^ 9^r ^c 

■\&l^cW ^^^^•t<-^n^ ca^ (^mo cfn^Sf^j ^ 9^^C 'Jay ij ^^'i^ Jt^J^ru^C^y />«-^^^ Ay 



Book I 1'l.u.I.Parfl. 





Fig. 3. 




Fig.4. 



y Q: ^7 



Fi^.5. 



(I Eyx 






t y 



Fig. 7 




RT 



Fie: 8. 



Book I. Plate!. Part I. 




FicT.p. 




Fl 



'€ 



lO. A 



-%^ 





Bookl.Platein. Pai-tl. 





Fig 17. 



BoOK,l. Plate, IV. Part, I. 
F. 





G H I K L M 

./ / .- J c f 

p o.::::::n:::z:::n:::::::::n::::.::::D:::zD t 
e k i k. I 771 




Fl^. :26 



DEF 




■■\m. 



Fie;. 19- 



it 






C80 • 

THE 

FIRST BOO 

OF 

O P T I C K S 



• 



PART 11. 



PROP. I. THEOR. L 

The Thanomena of Colours in refraSed or refleBed Lioht 
are not caujed i>j new modifications of the Light variouf^ 
ly imfreftj according to the variom terminations of the 
LtQ-ht and Shadow, 



-""C 



The Proof i^y Experimenu. 

EX PER. L 

FOR if the Sun fliine into a very dark Chamber jr/o- 
through an oblong Hole F, whofe breadth is the "^ 
fixth or eighth part of an Inch, or fomething lefs; and 
his Beam FH do afterwards pafs firft through a very 
large Prifm ABC, diftant about 20 Feet from the 

L Hole, 



Hole, and parallel to it, and then (with its white part) 
through an oblong HoleH^ whofe breadth is about 
the fortieth or fixtieth part of an Inch.^ and which is 
made in a black opake Body G I, and placed at the 
diftance of two or three Feet from the Prifm, in a pa- 
rallel iituation both to the Prifm and to the former 
Hole, and if this white Light thus tranfmitted through 
the Hole H, fall afterwards upon a white Paper pt^ 
placed after that Hole H^ at the diftance of three or 
four Feet from it^ and there paint the ufual Colours of 
the Prifm, fuppofe red at t^ yellow at s, green at r, 
blue at q, and violet at p ; you may with an iron Wire, 
or any fuch like (lender opake Body, whofe breadth is 
about the tenth part of an Inch, by intercepting the rays 
at k, 1, m, n or o, take away any one of the Colours 
at t, s, r, q or p, whilft the other Colours remain up- 
on the Paper as before ; or with an obftacle fomething 
bi^er you may take away any two, or three, or four Co- 
lours together, the reft remaining: So that any one of 
the Colours as well as violet may become outmoft in 
the confine of the fhadow towards p, and any one of 
them, as well as red may become outmoft in the confine 
©f the fhadow towards t, and any one of them may alfo 
border upon the fhadow made within the Colours by 
the obftacle R intercepting fome intermediate part of; 
the Light ; and, laftly, any one of them by 4 being 
left alone may border upon the ftiadow on either hando - 
AH the Colours have themfelves indifferently to any, 
confines of fhadow, and therefore the differences of theie 
Colours from one another, do not arife from the diffe- 
rent confines of fhadow, whereby Liglit is varioufly 
modified as has hitherto been the Opinion of Philofo- 

pherSo 



[83]. 

phers. In trying thefe things 'tis to be obferved, that 
by how much the Holes F and H are narrower^ and the 
intervals between them, and the Prilm greater, and the 
Chamber darker, by fo much the better doth the Ex- 
periment lucceed ; provided the Light be not fo far 
diminifhed, but^ that the Colours at pt be fufficiently 
viiible. To procure a Prifm of folid Glafs large enough 
for this Experiment will be difficult, and therefore a 
prifmatick Veflel muft be made of polifhed Glafs-plates 
cemented together, and filled with TV'ater* ^ c^^^ ^.l. 

EX PER. 11. 

The Sun's Light let into a dark Chamber through Vig^ ^^ 
the round Hole F, half an Inch wide, paffed firft through 
the Prifm ABC placed at the Hole, and then through 
a Lens P T fomething more than four Inches broad, and 
about eight Feet diftant from the Prifm,and thence coa* 
verged to O the Focus of the Lens diftant from it about 
three Feet, and there fell upon a white Paper DE. If 
that Paper was perpendicular to that Light incident up-- 
on it, as 'tis reprelented in the pofture D E, all the Co- 
lours -upon it at O appeared w^^iite. But if the Paper 
being turned about an Axis parallel to the Prifm, be- 
came very much inclined to the Light as 'tis reprefen- 
ted in the pofitions d.e and ^^ _; the fame Light in the 
one cafe appeared yellow and red, in the other blue. 
Here one and the fame part of the Light in one and the 
•fame place, according to the various inclinations of the 
Paper, appeared in one cafe white, in another yellox^ 
or red, in a third blue, whilft the confine of Light and 

L 2 Shadow- 



o 



[B4] 

Shadow, and the refraftions of the Prifm in all thefe 
cafes remained the fame. 

EX PER. III. 

Such another Experiment may be more eafily tried^ 
as follows. Let a broad beam of the Sun's Light coming 
into a dark Chamber through a Hole in the Window 
Khut be refrafted by a large Prifm ABC, whofe re^ 
ffadincf Angle C is more than 60 degrees, and fo. foon 
as it comes out of the Prifm let it fall upon the white 
Paper DE glewed upon a ftitf plane, and this Light^ 
when the Paper is perpendicular to it, as 'tis reprefen-- 
ted in DE, will appear perfectly vyhiteupon the Paper, 
but when the Paper is very much inclined to it in fuch 
a manner as to keep always parallel to the Axis of the 
Prifm, the whitenefs of the whole Light upon the 
Paper will according to the inclination of the Paper 
this way, or that way, change either into yellow and 
red, as in the pofture de^ or into blue and violet, as 
in the pofture ^^ And if the Light before it fall upon 
the Paper be twice refrafted the fame way by two pa- 
rallel Prifms, thefe Colours will become the more con> 
fpicuous. Here all the middle parts of the broad beam 
of white Light which fell upon the Paper, did without 
any confine of fhadow to modify it, become coloured 
all over with one uniform Colour, the Colour being al- 
ways the famie in the middle of the Paper as at the 
edges, and this Colour changed according the various 
obliquity of the retleding Paper, without any change 
in the refradions or fhadow, or in the Light which 
fell upon the Paper, And therefore thefe Colours are 

to 



to be derived from forrte other caufe than the new mo- 
difications of Light by refraftions and Ihadows. 

If it be asked, What then is their caufe? I anfwer, ^ 
That the Paper in the pofture de , being more ob- 
lique to the more refrangible rays than to the lefs re- 
frangible ones, is more ftrongly illuminated by the lat- 
ter than by the former, and therefore the lefs refran- 
gible rays are predominant in the refleded Light. And 
wherever they are predominant in any Light they tinge 
it with red or yellow, as may in fome meafure appear by 
the firft Propofition of the firft Book,and will more fully 
appear hereafter. And the contrary happens in the 
polture of the Paper ^^ , the more refrangible rays be- 
ing then predominant which always tinge Light with 
blues and violets.- 

EX PER. iv; 

The Colours of Bubbles with which Children play^^' 
are various, and change their iituation variouily, with' 
out any refpeft to any confine of Ihadow. If fuch a 
Bubble be covered with a concave Glafs, to keep it from 
being agitated by any wind or motion of the Air, the 
Colours will flowly and regularly change their iitua- 
tion, even whilft the Eye, and the Bubble, and all Bo- 
dies which emit any Light, or caft any fliadow, re- 
main unmoved. And therefore their Colours arife from 
fome regular caufe which depends not on any confine of 
ihadow. What this caufe is will be ftiewedin the next 
Book. 

To 



8^ 

To thefe Experiments may be added the tenth Ex- 
periment of the firft Book, where the Sun's Light in a 
dark Room being traje£ted through the parallel fuperfi- 
cies of two Prifms tied together in the form of a Paral- 
lelopide, became totally of one uniform yellow or red 
Colour, at its emerging out of the Prifms. Here, in 
the produdion of thefe Colours, the confine of fhadow 
can have nothing to do. For the Light changes from 
white to y ellow,orange and red fucceffively,withoutany 
alteration of the confine of fhadow: And at both edges of 
the emerging Light where the contrary confines of fha- 
dow ought to produce different etfeds, the Colour is 
one and the fame, whether it be white, yellow, orange 
or red : And in the middle of the emerging Light, 
where there is no confine of fhadow at all, the Colour 
is the very fame as at the edges, the whole Light at its 
very firfl emergence being of one uniform Colour, whe- 
ther white, yellow, orange or red, and going on thence 
perpetually without any change of Colour, Inch as the 
confine of fhadow is vulgarly fuppofed to work in tc- 
fraited Light after its emergence. Neither can thefe 
Colours arife from any new modifications of the Light 
by refrafldons, becaufe they change fucceffively from 
wMte to yellow, orange and red, while the refradions 
remain the faine, aiad alfo becaufe the refraftions are 
made contrary ways by parallel fuperficies which de- 
flroy on€ anothers effefts. They arife not therefore 
from any modifications of Light made by rcfradions 
itnd fhadow^, but have fome other caufe. What that 
caufe is we fhewed above in this tenth Experiment, 
and need not here repeat it. 

There 



^7l 

There is yet another material circuinftance of this 
Experiment* For this emerging Light being by a third Fig. 22.- 
Prifm H I K refraded towards the Paper PT-> and there Tart i . 
painting the ufual Colours of the Prifm^ red^ yellow, 
green, blue, violet : If thefe Colours arofe from the 
refradions of that Prifm modifying the Light, they 
woald not be in the Light before its incidence on that 
Prifm. And yet in that Experiment we found that 
when by turning the two firft Prifms about their com- 
mon Axis all the Colours were made to vanifli but the 
red ; the Light which makes that red being left alone, 
appeared of the very fame red Colour before its inci« 
dence on the third Prifm. And in general we find by 
other Experiments that when the rays which differ in 
refrangibility are feparated from one another, and any 
one fort of them is confidered apart, the Colour of the 
Light which they compofe cannot be changed by any 
refraftion or reflexion whatever, as it ought to be were 
Colours nothing elfethan modifications of Light caufed 
by refraftions, and reflexions, and lliadows. This un» 
changeablenefs of Colour I am now to defcribe in the 
following Propofition, 

PROP. IL THEOR. IL 

j^ll honiogeneal Light has its frofer Colour anfwering to^ 
its degree of refrangiiility^ and that Colour cannot he 
changed by rejlexions and reffa<^ionSs 

In the Experiments of the 4.th Propofition of the firft 
Book, when I had feparated the heterogeneous rays 
from one another, the Spectrum pt formed by the fepa- 
rated 



[ 88 ] 

rated rays^ did in the progrefs from its end p, on which 
the moft refrangible rays fell, unto its other end t, on 
which the leaft refrangible rays fell, appear tinged with 
this Series of Colours, violet, indico, blue, green, yel- 
low, orange, red, together with all their intermediate 
degrees in a continual fucceffion perpetually varying : 
So that there appeared as many ii^gi-^ees ^ Colours, as M 
there were forts of rays differing in refrangibility. /?r /-^y/^ 

EXP E R. V. 

Now that thefe Colours could not be changed by re- 
fradion, I knew by refrading with a Prifm fometimes 
one very little part of this Light, fometimes another 
very little part, as is defcribed in the 1 2 th Experiment 
of the fir ft Book. For by this refradion the Colour of 
the Light was never changed in the leaft. If any part 
of the red Light was refraded, it remained totally of 
the fame red Colour as before. No orange, no yel- 
lov/, no green, or blue, no other new Colour was pro- 
duced by that refraflion. Neither did the Colour any 
ways change by repeated refradlions, but continued al- 
ways the fame red entirely as at firft. The like con- 
ftancy and immutability 1 found alfo in the blue, green, 
and other Colours. So alfo if I looked through a Prifm 
upon any body illuminated with any part of this homo- 
geneal Light, as in the i^th Experiment of the firft 
Book is defcribed j I could not perceive any new Co- 
lour generated this way. All Bodies illuminated with 
compound Light appear through Prifms confufed ( as 
was faid above ) and tinged with various new Colours^ 
but thofe illuminated with homogeneal Light appeared 

throuiih 



through Priinis neither lets dlftinfl:., nor otherwife co- 
loured, than when viewed with the naked Eyes. Their 
Colours were not in the leaft changed by the refradion 
of the interpofed Priim. I fpeak here of a fenfible 
change of Colour : For the Light which I liere call ho» 
mogeneal, being not abfolutely homogeneal, there ought 
to arife fome little change of Colour from its heteroge- 
neity. But if that heterogeneity was fo little as it might 
be made, by the faid Experiments of the fourth Propo- 
fition, that change was not fenfible, and therefore, • in 
Experiments where fenfe is judge, ought to be accoun- 
ted none at all. 

EXPERo VL 

And as thefe Colours were not changeable by refra- ^ 
(ftions, fo neither were they by reflexions. For all 
white, grey, red.» yellow, green, blue, violet Bodies, as 
Paper, Allies, red, Lead, Orpiment, Indico, Bile, Gold, 
Silver, Copper, Grafs, blue Flowers, Violets, Bubbles 
of Water tinged with various Colours, Peacock's Fea- 
thers, the tinfture of Lignum Mefhriticum^ and fuch 
like, in red homogeneal Light appeared totally red, in 
blue Light totally blue, in green Light totally green, 
and fo of other Colours. In the homogeneal Light of 
of any Colour they all appeared totally of that fame 
Colour, with this^nly difference, that fome of them 
tefleded that Light more ftrongly, others more faintly. 
1 never yet found any Body which by reflefting homo- 
peneal Light could fenfibly change its Colour. 

M From 



M^ 



From all which it is manifeft, that if the Sun's Light 
confifted of but one fort of rays, there would be but 
one Colour in the whole World, nor would it be pof- 
iible to produce any new Colour by reflexions and re- 
fractions, and by confequence that the variety of Co- 
lours depends upon the compoiition of Light, 

"DEFINIT ION. 

The homogeneal light and rays which appear red,, 
or rather make Objefts appear fo, I call rubrific • 
or red-makng ; thofe which make ObjeSs appear 
yellow, green, blue and violet, I call yellow-ma- 
king, green-makingi, blue-making, violet-making, 
and fo of the reft. And if at any time I fpeak of: 
light and rays as coloured or endued with Co- 
lours, I would be underftood to fpeak not philo- 
fophically and properly, but groily, and accor- 
ding to fuch conceptions as vulgar People in fee- 
ing all thefe Experiments would be apt to frame. - 
For the rays to fpeak properly are not coloured^- 
In them there is nothing elfe than a certain power 
and difpofition to ftir up a fenfation of this or that 
Colour. For as found in a Bell ori mufical Stringy, 
or other founding Body, is nothing but a trem- 
bling Motion, and in the Air nothing but that 
Motion propagated from the Object, and imthe 
Senforium 'tis a fenfe of that Motion under the 
form of found; fo Colours in theObjeft are no- 
thing but a difpotition to reflet this or that fort 
of rays more copioully than the reft ; in the rays 
they are nothing but their difpofitions to propa- 
gate 



gate this or that Motion into the Senibrium, and 
in the Senfbrium they are fenfations of thofe Mo- 
tions under the forms of Colours. ^ 

PROP. III. PROB. I. 

To define the refrangiiility of the feveral joints of homo^ 
geneal Light anjis>jertng to the feveral Colours. 

For determining this Problem I made the following 
Experiment. 

EXPER. Vll. 

' When I had caufed the redilinear line iides A F, G M, Kg-, 4.. 
of the Spedlrum of Colours made by the Prifm to be 
diftindly denned, as in the fifth Experiment of the 
firft Book is defcribed, there were found in it all the 
homogeneal Colours in the fame order and fituation 
one among another as in the Speftrum of fimple Light^ 
defcribed in the fourth Experiment of that Book. For 
the Circles of which the Speftrum of compound Light 
PT is com.pofed, and which in the middle parts of 
the Spectrum interfere and are intermixt with one ano- 
ther, are not intermixt in their outmoft parts where 
they touch thofe reftilinear fides A F and G M. And 
therefore in thofe redilinear fides when diftinftly defi- 
ned, there is no new Colour generated by refraction. I 
obferved alfo, that if any where between the two out- 
moft Circles TMF and PGA a right line, as y^v, was 
crofs to the Spedrum, lb as at both ends to fall per- 
pendicularly upon its redtilinear fides, there appeared , 

M a one 



'■■2 



one and the iliiiie Colour and degree of Colour from one 
end of this line to the other. I delineated therefore in 
a Paper die perimeter of the Speitrum F APGMT, 
and in trying the third Experiment of the firft Book, I 
held the Paper fo that the Spearum might foil upon 
this delineated Figure, and agree VN^ith it exaftly, whilft 
an AiTiftant whofe Eyes for diftinguifliing Colours were 
more critical than mine, did by right Vims ^cpo, yc\ ,'0-c. 
drawn crofs the Spedrum, note the confines of the Co- 
lours that isof the red M^.^F of theorange<x7^^^, of 
the yellow y^?^, of the green =- ^ H' , of the blue ^^xS^, 
of the indico ^x^ux, and of the violet xQAm. And 
this operation being divers times repeated both in the 
lame and in feveral Papers , I found that the Ob- 
fervations agreed well enough with one another, and 
that the redilinear fides M G and FA were by the faid 
crofs lines divided after the manner of a mufical Chord. 
Let GM be produced to X, that MX may be equal 
toGM, and conceive GX, xX, 'X, ''X, ^X, yX, «X^ 
MX,, to be in proportion to one another, as the num- 
bers I, I,. ^5 -^ p I? ?6' i' ^^i fo ^^ reprefent the 
Chords of the Key, and of a Tone, a third Minor, a 
fourth, a fifth, afixthMajor, aTeventh,, and aa eighth 
above that Key : And the intervals M ^ ? ^ 7 , / ^ j^/- « , 71 ' ,. 
^>^, andxG, will be the fpaces which the feveral Co- 
lours ( red, orange,„yellow, green, blue, indico, violet ), 
take up. 

Now thefe intervals or fpaces- fubtending the diffe- 
rences of the refraftions of the rays going to the limits, 
of thofe Colours, tliat isi> to the points M, a, 7, c^ /;,/, x, G5. 
may without any fenfi.ble Error be accounted propor- 
tional to the differences of the fines of refraftion of thofe 

rays 



93 

rays having one common fine of incidence, and there- 
fore fince the common fine of incidence of the mod and 
leafi: refrangible rays out of Glafs into Air was, (by a 
method defcribed above ) found in proportion to their 
fines of refradion, as 50 to 77 and 78, divide the dif- 
ference between the fines of refradion 77 and 78, as the 
line G M is divided by thofe intervals, you will have 

11-f 11\^ 11\' llh^ 77i. 773' 779,78, the fi_nes of 
refraction of thole nlys out of Glais into Air, their 
common fine of incidence being 50. So then the fines 
of the incidences of all the red-making rays out of 
Glafs into Air, were to the fines of their refraftions, 
not greater than 50 to 77, nor lefs than 50 to 77J-, but 
varied from one another according to all interme- 
diate Proportions. And the fines of the incidences 
of the green-making rays were to the fines of 
their refraftions in all proportions from that of 50 
to 77^, unto that of 50 to 77^. And by the like limits 
above-mentioned were the refradions of the rays be- 
longing to the reft of the Colours defined, .the fines of 
the red-making rays extending from 77 to 773- , thofe 
of the orange-making from 77^ to 77^ , thofe of the yel- 
low-making from 77J to 77 J, thofe of the green-making 
from 77f to 77^5 thofe of the blue-making from 77^ to 
77]^, thofe of the indico-making from 77-^ to 77^-, and 
thofe of the violet from 77^ to 78, . 

Thefe are the Laws of the refradions made out of 
Glafs into Air, and. thence by the three Axioms of tiie 
iirft Book the Laws of the refradions made out of Air 

into Glafs are eafilv derived. 

J.. 

E X P E R, 



94] 



EXPER. VIII. 

I found moreover that when Light goes out of Air 
through feveral contiguous refracting Mediums as 
through Water and Glafs, and thence goes out again 
into Air, whether the-refrafting fuperficies be parallel 
or inclined to one another, that Light as often as by- 
contrary refractions 'tis fo corrected, that it emergeth 
in lines parallel to thofe in which it was incident, 
continues ever after to be white. But if the emer- 
gent rays be inclined to the incident, the whitenefs of 
the emerging Light will by degrees in paffing on from 
the place of emergence, become tinged in its edges with 
Colours. This I tryed by refra£ting Light with Prifms 
of Glafs within a prifmatick Veffel of Water. Now thofe 
Colours argue a diverging and feparation of the hetero- 
geneous rays from one another by means of their un- 
equal refractions, as in what follows will more fully 
appear.* And, on the contrary, the permanent white- 
nefs argues, that in like incidences of the rays there is 
no fuch feparation of the emerging rays, and by confe- 
quence no inequality of their whole refraCtions. Whence 
i leem to gether the two following Theorems. 

^ I . The Exceffes of the fines of refraCtion of feveral 
forts of rays above their common fine of incidence when 
the refractions are made our of divers denfer^^edjums 
immediately into one and the fame rarer medium,^'^afe 
to one another in a given Proportion. ^f^m^<;^i- ^^^i- f' 

^^y' f'^^ ji^^ 'yvo-^ eac-^iat^^' 



*»e *^ 



[9S] 

a. The Proportion of the fine of incidenceto the fine 
of refraftion of one and the fame fort of rays out of one 
medium into another, is compofed of the Proportion of 
the fine of incidence to the fine of refraSion out of the 
firft medium into any third medium, and of the Pro- 
portion of the fine of incidence to the fine of refraftion 
out of that third medium into the fecond medium. 

By the firft Theorem the refraftions of the rays of 
every fort made out of any medium into Air are known 
by having the refraction of the rays of any one fort. As 
for inftance, if the refraftions of the rays of every Ibrt 
out of Rain-water into Air be defired, let the common 
fine of incidence out of Glafs into Air be fubduded 
from the fines of refradion, and the Exceffes will be 

^7i ^7«-' ^7?' .^7^^7i' ^7h ^79% ^^^ Suppofenow 
that the fine of incidence of the leaft refrangible rays be 
to their fine of refradion out of Rain- water into Air as 
three to four, and fay as i the difference of thofe fines 
is to 3, the fine of incidence, fo is 27 the leaft of the 
Exceffes above-mentioned to a fourth number 81 ; and 
81 will be the common fign of incidence out of Rain- 
water into Air, • to which fine if you add all the above- 
mentioned Exceffes you will have, the defired fines of 
the refradions 108^^. loSs ?. loSf, loSf, io8f, io8f^, 
io8i, 109. 

By the latter Theorem the refradion out of one me- 
dium into another is gathered as often as you have 
the refraftions out of them both into any third medium^ 
As if the fine of incidence of any ray out of Glafs into 
Air be to its fine of refraction as ao to 3 1, and the fine 
of incidence of the fame ray out of Air into Water, be 

to 



[96] 

'to its fine of refradion as four to three; the fine of 
incidence of that ray out of Glafs into Water will be to 
its fine of refraction as a o to 31 and 4 to ^ joyntly, that 
is, as the FaCtum of 20 and 4. to the Faftum of 3 1 and 
5, or as 80 to 95. 

And thefe Theorems being admitted into Opticks, 
there would be fcope enough of handling that Science 
voluminoufly after a new manner ; not only by teaching 
thofe things which tend to the perfeftion of vifion, but 
alfo by determining mathematically all kinds of Phaeno- 
mena of Colours which could be produced by refra- 
fbions. For to do this, there is nothing elfe requifite 
than to find out the reparations of heterogeneous rays, 
and their various mixtures and proportions in every 
mixture. By this way of arguing I invented almoft 
all the Pha^nomena defcribed in thefe Books, befide fome 
others lefs necefifary to the Argument ; and by the 
fucceffes I met with in the tryals, I dare promife, that 
to him who fhali argue truly, and then try all things 
with good Glaffes and fufficient circumfpeftion, the 
expefted event will not be wanting. But he is firft to 
know what Colours will arife from any others mixt in 
.any affigned Proportion. 

PROP. IV. THEOR. III. 

^Colours ma^ he produced hy comfofitiGn "which JhaU he like 
to the Colours of homogeneal Light as to the affear'ance 
of Colour^ hut not as to the immutahtlity of Colony^ and 
c'onjlttution of Light, ^nd thofe Colows h'j ho'w ?nuch 
they are more compounded hy fo much are they lejs fuU 
..and inteufe.^ and hy too much comfofition they may he 



I 



diluted and -z^eakened till the^ ceafe.^ ^!Z be?'e may be 
aljo Colours froduced by comfofition^ ^juhich arc not fully 
like any of the Colours of homogeneal Light, y 

For a mixture of homogeneal red and yellow com- ^ 
pounds an orange^ like in appearance of Colour to that 
orange which in the feries of unmixed prifmatick Co- 
lours lies between them ; but the Light of one orange 
is homogeneal as to refrangibility^ that of the other is 
heterogeneal, and the Colour of the one , if viewed 
through a Prifm, remains unchanged, that of the other 
is changed and refoived into its component Colours red 
and yellow. And after the fame manner other neigh- 
bouring homogeneal Colours may compound new Co- 
lours, like the intermediate homogeneal ones, as yel- 
low and green, the Colour between them both, and af- 
terwards, if blue be added, there will be made a green 
the middle Colour of the three which enter the compo- 
fition. For the yellow and blue on either hand,if they are 
equal in quantity they draw the intermediate green equal- 
ly towards themfeives in compofition, and fo keep it as 
it were in equilibrio, that it verge not more to the 
yellow on the one hand, than to the blue on the other, 
but by their mixt actions remain ftill a middle Colour. 
To this mixed green there may be further added 
fome red and violet^ and yet the green will not prefent- 
ly ceafe but only grow lefs full and vivid, and by in- 
creafing the red and violet it will grow more and more 
dilute, until by the prevalence of the added Colours it 
be overcome and turned into whitenefs, or fome other 
Colourc So if to the Colour of any homogeneal Light, 
the Sun's white Light compofed of all forts of rays be 

N added. 



[98] 

added^ that Colour will not vaniih or change its fpe- 
cies but be diluted, and by adding more and more white 
it will be diluted more and more perpetually. Laft- 
ly, if red and violet be mingled, there will be generated 
according to their various Proportions various Purples, 
fuch as are not like in appearance to the Colour of any 
homogeneal Light, and of thefe Purples mixt with yel-- 
low and blue may be made other nev^ Colours.. 

PROP. V. THE OR. IT. 

Whitenejs and all grey Colours bet'ween ^white and ifach^.. 
may be compounded of Colours^ and the isohttenejs of the 
Suns Light is compunded of all the frimary Colours 
mixt in a due p^o fort ion. ■-, 

The Troofhy Experiments. 

EXP E R, IX. 

Fig' 5. The Sun fhining into a dark Chamber through a 
little round Hole in the Window Ihut, and his Light 
being there refracted by a Prifm to caft his coloured- 
Image P T upon the oppofite Wall : I held a white Pa- 
per V to that Image in fuch manner that it might be 
illuminated by the coloured Light retieSed from thence, 
and yet not intercept any part of that Light in its paf- 
fage from the Prifm to the Speftrum. And I found that 
when the Paper was held nearer to any Colour than to 
the reft, it appeared of that Colour to which it ap- 
proached nearcft ; but when it was equally or almoft 

equally 



[99] 

equally diftant from all the Colours, Co that it might 
be equally illuminated by them all it appeared white. 
And in this lafl: lituation of the Paper, if ibme Colours 
were intercepted, the Paper loft its white Colour, and 
appeared of the Colour of the reft of the Light which 
was not intercepted. So then the Paper was illuminated 
with Lights of various Colours, namely, red, yellow, 
green, blue and violet, and every part of the Light re- 
tained its proper Colour, imtil it w^as incident on the 
Paper, and became reflected thence to the Eye ; fo that 
if it had been either alone (the reft of the Light being 
intercepted) or if it had abounded moft and been pre- 
dominant in the Light reflected from thePaper,it would 
have tinged the Paper with its own Colour; and yet be- 
ing mixed with the reft of the Colours in a due propor* 
tion, it made the Paper look white, and therefore by a 
compofition with the reft produced that Colour. The 
feveral parts of the coloured Light reflefted from the 
Spe(3:rum,whilft they are propagated from thence thro' 
the Air, do perpetually retain their proper Colours^ 
becauie wherever they fall upon the Eyes of any Specta- 
tor, they make the feveral parts of the Spectrum to 
appear under their proper Colours. They retain there- 
fore their proper Colours when they fall upon the Pa- 
per V, and lb by the confufion and perfed mixture of 
thofe Colours compound the whitenefs of the Light 
reflected from thence. 

E X P E R. X* 

Let that Speftrum or folar Image P T fall now upon Fig» 6, 
the Lens M N above four Inches broad, and about fix 

N 2 Feet 



[ lOO ] 

Feet diftant from the Piifm ABC, and fo figured that 
it may caufe the coloured Light which divergeth from 
the Prifin to converge and meet again at its Focus G, 
about fix or eight Feet diftant from the Lens, and 
thereto fall perpendicularly upon a vv^iite Paper DE. 
And if you move this Paper to and fro, you will per- 
ceive that near the Lens, as at de^ the whole folar Image 
(fuppofe at pt) will appear upon it intenfly coloured 
after the m.anner above-explained, and that by receding 
from the Lens thofe Colours will perpetually come to- 
wards one another, and by mixing more and more di- 
lute one another continually, until at length the Paper 
come to the Focus G, where by a perfed: mixture they 
will wholly vanifh and be converted into whitenefs, the 
whole Light appearing now upon the Paper like a little 
white Circle. And afterwards by receding further from 
the LenSj the rays which before converged will now 
crofs one another in the Focus G, and diverge from 
thence, and thereby make the Colours to appear again, 
but yet in a contrary order ; fuppofe at o\ , where the 
red t is now above which before was below, and the 
violet p is below which before was above. 

Let us now flop the Paper at the Focus G where 
the Light appears totally white and circular, and let us 
confider its whitenefs. I fay, that this is compofed of 
ihe converging Colours. For if any of thofe Colours 
be intercepted at the Lens, the whitenefs will ceafe and 
degenerate into that Colour which arifeth from the 
compofition of the other Colours which are not inter- 
cepted. And then if the intercepted Colours be let 
pafs and fall upon that compound Colour, they mix 
with it, and by their mixture reftore the whitenefs. 

So 



[ lOI ] 

So if the violet, blue and green be intercepted^ the re- 
maining yellow, orange and red will compound upon 
the Paper an orange, and then if the intercepted Co- 
lours be let pafs they will fall upon this compounded 
orange, and together with it decompound a white. So 
alfo if the red and violet be intercepted, the remaining 
yellow, green and blue, will compound a green upon 
the Paper, and then the red and violet being let pafs 
will fall upon this green, and together with it decom- 
pound a w^hite. And that in this compofition of white 
the feveral rays do not fuifer any change in their colori- 
fic qualities by acting upon one another, but are only 
mixed, and by a mixture of their Colours produce 
white, may further appear by thefe Arguments. 

If the Paper be placed beyond the Focus G, fuppofe 
at ^-'?, and then the red Colour at the Lens be alternate^ 
ly intercepted, and let pafs again, the violet Colour on 
the Paper vvdll not fuffer any change thereby, as it ought 
to do if the feveral forts of rays aded upon one another 
in the Focus G, where they crofs. Neither will the 
red upon the Paper be changed by any alternate flop- 
ping, and letting pafs the violet which croffeth it. 

And if the Paper be placed at the Focus G, and the 
wdiite round Ima2,e at G be viewed through the Prifm 
HIK, and by the refradion of that Prifm be tranflated 
to the place rv, and there appear tinged with various 
Colours, namely, the violet at v and red at r , and 
others between, and then the red Colour at the Lens be 
often ftopt and let pafs by turns, the red at r will ac- 
cordingly difappear and return as often, but the violet 
at v will not thereby fuifer any change. And lb by 
flopping and letting pafs alternately the blue at the 

Lens^ 



[102] 

Lens^ the blue at r will accordingly dlfappear and re- 
turn, v/ithout any change made in the red at r. The 
red therefore depends on one fort of rays, and the qlue 
on another fort, which in the Focus G where they are 
commixt do nota£b on one another. And there is the 
fame reafon of the other Colours. 

I coniidered further, that when the moft refrangible 
raysPp, and the leaft refrangible ones Tt, are by con- 
verging inclined to one another, the Paper, if held very 
oblique to thofe rays in the Focus G, might refled one 
fort of them more copioufly than the other fort, and by 
that means the refledted Light would be tinged in that 
Focus with the Colour of the predominant rays, pro- 
vided thofe rays feverally retained their Colours or co- 
lorific qualities in the compofition of white made by 
them in that Focus. But if they did not retain them 
in that white, but became all of them feverally endued 
there with a difpofition to ftrike the fenfe with the per- 
ception of white, then they could never lofe their v/hite- 
nefs by fuch reflexions. I inclined therefore the Paper 
to the rays very obliquely, as in the fecond Experiment 
of this Book, that the moft refrangible rays might be 
more copioully refleded than the reft, and the white- 
nefs at length changed fucceflively into blue, indico 
and violet. Then I inclined it the contrary way, that 
the moft refrangible rays might be more copious in the 
reflected Light than the reft, and the whitenefs turned 
fucceflively to yellow, orange and red. 

Laftly, I made an Inftrument X Y in fafliion of a 
Comb, whofe Teeth being in num.ber fixtecn were 
about an Inch and an half broad, and the intervals of the 
Teeth about two Inches wide. Then by interpofing 

fuc- 



fecceflively the Teeth of this Inftrument near tlie Lens 
I intercepted part of the Colours by the interpofed 
Tooth, whilft the reft of them went on through the in- 
terval of the Teeth to the Paper D E, and there pain- 
ted a round folar Image. But the Paper I had firft pla- 
ced fo, that the Image might appear white as often 
as the Comb was taken away; and then the Comb be- 
ing as was faid interpofed, that whitenefs by reafon of 
tlie intercepted part of the Colours at the Lens did al- 
ways change into the Colour compounded of thofe 
Colours which were not intercepted, and that Colour 
was by the motion of the Comb perpetually varied fo 
that in the palling of every Tooth over the Lens all . 
thefe Colours red, yellow, green, blue and purple, did 
always fucceed one another. I caufed therefore all the 
Teeth to pafs fucceffively over the Lens, and when the 
motion was How, there appeared a perpetual fucceflion 
of the Colours upon the Paper : But if I fo much acce- 
lerated the motion, that the Colours by reafon of their 
quick fucceflion could not be diftinguillied from one 
another,, the appearance of the fingle Colours ceafed»- 
There was no red, no yellow, no green, no blue, nor 
purple to be feen any longer, but from a confufion of 
them all there arofe one uniform white Colour. Of the 
Light which now by the mixture of all the Colours ap- 
peared white, there was no part really white. One 
part was red, another yellow, a third green, a fourth 
blue, a fifth purple, and every part retains its proper 
Colour till it ftrike the Senibrium. If the impreflions 
follow one another f lowly, fo that they may be feve- 
rally perceived, there is made a diftinft fenfation of all 
the Colours one after another in a continual fucceflion. 

But 



[104] 

But if the impreffions follow one another fo quickly 
that they cannot be feverally perceived^ there arifetk 
out of them all one common feniation, which is nei- 
ther of this Colour alone nor -of that alone, but hath it 
felf indifferently to 'em all, and this is a feniation of 
whitenefs. By the quicknefs of the fucceffions the im- 
preffions of the feveral Colours are confounded in the 
Senforium, and out of that confuiion arileth a mixt fen- 
_)(. fation. If a burning Coal be nimbly moved round in a 
Circle with Gyrations continually repeated, the whole 
Circle will appear Uke fire 3 the reafon of which is, that 
the fenfation of the Coal in the feveral places of that 
Circle remains impreft on the Senforium, until the 
Coal return again to the &me place. And fo in a 
quick confecution of the Colours the impreffion of every 
Colour remains in the Senforium, until a revolution of 
all the Colours be compleated, and that firft Colour re- 
turn a^ain. The impreffions therefore of all the fucceffive 
Colours are at once in theSenforium,and joyntly ftir up 
a fenfation of them all ; and fo it is manifeil by this Ex- 
periment, that the commixt im-preffions of all the Co- 
lours do ftir up and beget a feniation of white, that is, 
that whitenefs is compounded of all the Colours. 

And if the Comb be now taken away, that all the 
Colours may at once pafs from the Lens to the Paper, 
and be there intermixed, and together retie£ted thence 
to the Speftators Eyes ; their impreffions on the Senfo- 
rium being now more fubtily^ and perfedly commixed 
there, ought much m.ore to ftir up a fenfation of white- 



You 



105 ] 

You may inftead of the Lens uie two Prifms HIK 
andLMN, which by refrafting the coloured Light 
the contrary way to that of the firft refraflion, may 
make the diverging rays converge and meet again in G, 
as you fee it reprefented in tlie feventh Figure. For Fig- 7. 
where they meet and mix they will compofe a white 
Light as when a Lens is ufed. 

EX PER. XL 

Let the Sun's coloured Image PT fall upon the Wall F%. 8, 
of a dark Chamber, as in the third Experiment of the 
firft Book, and let the fame be viewed through a Prifm 
a b c, held parallel to the Prifm ABC, by whofe refra- 
Sion that Image was made, and let it now appear lower 
than before, fuppofe in the place S over againft the red- 
colour T. And if you go near to the Image PT, the 
Spedrum S will appear oblong and coloured like the 
Image P T ; but if you recede from it, the Colours of 
the Speftrum S will be contracted m.ore and more, and 
at length vanifh, that Speftrum S becoming perfedly 
round and white ; and if you recede yet further, the 
Colours will emerge again, but in a contrary order. 
Now that Spedrum S appears white in that cafe when 
the rays of feveral forts which converge from the feve- 
ral parts of the Image PT, to the Prifm a be, are fo 
refracted unequally by it, that in their paffage from the 
Prifm to the Eye they may diverge from one and the 
faine point of the Spedrum S, and fo fall afterwards 
upon one and the fame point in the bottom of the Eye^ 
and there be mingled. 

O And 



And further, if the Comb be here made ufe of, by- 
whofe Teeth the Colours at the Image PT may be fuc- 
ceffiveiy intercepted ; the Speftrum S when the Comb 
is moved flowly will be perpetually tinged with fuc- 
ceffive Colours : But when by accelerating the motion 
of the Comb, thefucceffion of the Colours is fo quick 
that they cannot be feverally feen, that Spe£trum S, by 
a confufedand mixt fenfationof them all, will appear 
white. 

EXPER. XIL 

Fio', Q. The Sun fliining through a large Prifm ABC upon 
aCombXY, placed immediately behind the Prifm., his 
Light which paffed through the interftices of the Teeth 
fell upon a white Paper D E. The breadths of the 
Teeth were equal to their interftices, and j^tven Teeth 
together with their interftices took up an Inch in 
breadth. Now when the Paper was about two or 
three Inches diftant from the Comb, the Light which 
paffed through its feveral interftices painted fo many 
ranges of Colours kl, mn, op, qr, l5)'r. which were 
parallel to one another and contiguous, and without any 
mixture of white. And thefe ranges of Colours, if the 
Comb was moved continually up and down with a re- 
ciprocal motion, afcettded and defcended in the Paper^, 
and when the motion of the Comb was fo quick, that 
the Colours could not be diftinguiftied from one another^ 
the v/hole Paper by their confufion and mixture in the 
Senforium appeared white. 

Let 



[ro;] 

Let the Gomb now reft, and let the Paper be remo- 
ved further from the Prifm, and the feveral ranges of 
Colours will be dilated and expanded into one another 
more and more, and by mixing their Colours will di- 
lute one another, and at length, when the diftance 
of the Paper from the Comb is about a Foot , or a 
little more ( fuppofe in the place i D 2 E ) they will 
fo far dilute one another as to become white. 

With any Obftacle let all the Light be now ftopt 
which pafles through any one interval of the Teeth, fo 
that the range of Colours which comes from thence may 
be taken away, and you will fee the Light of the reft of 
the ranges to be expanded into the place of the range 
taken away, and there to be coloured. Let the inter- 
cepted range pafs on as before, and its Colours falling 
upon the Colours of the other ranges, and mixing with 
them, will reftore the whitenefs. 

Let the Paper a D a E be now very much inclined to 
the rays, fo that the moft refrangible rays may be more 
copiouily refleded than the reft, and the white Colour 
of the Paper through the excefs of thofe rays will be 
changed into blue and violet. Let the Paper be as 
much inclined the contrary way, that the leaft refran- 
gible rays may be now morq copioufly reflefted than 
the reft, and by their excefs the whitenefs will be 
changed into yellow and red. The feveral rays there- 
fore in that white Light do retain their colorific qua- 
lities, by which thofe of any fort, when-ever they be- 
come more copious than the reft, do by their excefs 
-and predominance caule their proper Colour to ap- 
pear. 

O a ^ And 



io8 

And by the flime way of arguing, applied to the third 
Experiment of this Book, it may be concluded, that 
the white Colour of all refrafted Light at its very firft 
emergence, where it appears as white as before its inci- 
dence, is compounded of various Colours. 

EXPER. XIII. 

In the foregoing Experiment the feveral intervals of 

the Teeth of the Comb do the office of fo many Prifms^ 

every interval producing the Phgenomenon of one Prifm, 

Whence inftead of thofe intervals ufing feveral Prifms, I 

try 'd to compound whitenefs by mixing their Colours,and 

did it by ufing only three Prifms, as alfo by ufing only 

Fio\ 10. two as follows. Let two Prifms ABC and a be, whole 

refrafting Angles B and b are equal,be fo placed parallel 

to one another, that the refradting Angle B of the one 

may touch the Angle c at the bafe of the other, and 

their planes C B aiid cb, at which the rays emerge, may 

lye in diredum. Then let the Light trajeded through 

: them fall upon the Paper M N, diftant about 8 or 12 

Inches from the Prifms. And the Colours generated 

by the interior limits B and c of the two Prifms, will 

be mingled at PT.^ and there compound white. For if 

either Prifm be taken away, the Colours made by the 

other vs^ill appear in that place PT, and when the Prifm 

is reftored to its place again, fo that its Colours may 

there fall upon the Colours of the other, the mixture 

of them both will reftore the whiteneise 

This 



[ lop] 

This Experiment fucceeds alio, as I have tryed^whai 
the Angle b of the lower Prifm, is a little greater than 
the An^le B of the upper , and between the interior 
Angles B and c, there intercedes fome fpace B c, as is 
reprefented in the Figure, and the refrafting planes 
BC and be, are neither in direftum, nor parallel to 
one another. For there is nothing more requifite to 
the fuccefs of this Experiment^ than that the rays of all 
forts may be uniformly mixed upon the Paper in the 
place FT. If the moft refrangible rays coming from 
the fuperiorPrifm take up all thefpace from M to P, the 
rays of the fame fort which come from the inferier 
Prifm ought to begin at P, and take up all the reft of the 
fpace from thence towards N. If tlie lea ft refrangible 
rays coming from the fuperior Prifm take up the fpace 
MT,. the rays of the fame kind which come from the 
other Prifm ought to begin at T, and take up the remain^ 
ing fpace T N. If one ibrt of the rays which have in- 
termediate degrees of refrangibility, and come from the 
fuperior Prifm be extended through the fpace MQ, and 
another fort of thofe rays through the fpace MR, and 
a third ibrt of them through the fpace MS, the fame 
forts of rays coming from the lower Prifm, ought to il^ 
luminate the remaining fpaces QN, RN, SN refpe- 
ftively. And the fame is to be underftood of all the 
other forts of rays. For thus the rays of every fort will 
be fcattered uniformly and evenly through the whole 
fpace MN, and ih being every where mixt in the fame 
proportion, they mufl every where produce the lame 
Colour. And therefore fince by this mixture they pro- 
duce white in the exterior fpaces MP and TN, they 
lEuft alfo produce white in the interior ipace P T» This 

is 



Is the reaTon of the compofition by v/hich whitenefs 
was produced in this Experiment, and by what other . 
way foever I made the like compofition the refult was J 
whitenefs. '^ 

Laftly, If with the Teeth of a Comb of a due fize, 
the coloured Lights of the two Prifms which fall upon 
the fpace PT be alternately intercepted , that fpace 
PT, when the motion of the Comb is flow, will always 
appear coloured, but by accelerating the motion of 
the Comb fo much, that the fucceflive Colours can- 
not be diftinguiflied from one another, it will appear 
white. 

EXPER. XIV. 

^^-: Hitherto I have produced whitenefs by mixing the 
Colours of Prifms. If now the Colours of natural Bo- 
dies are to be mingled, let Water a little thickned with 
Soap be agitated to raife a froth, and after that froth 
has flood a little, there will appear to one that fliall 
view it intently various Colours every v/here in the 
furfaces of the feveral Bubbles ; but to one that fhall 
go fo far off that he cannot diftinguifli the Colours from 
one another, the whole froth will grow white with a 
perfect whitenefs. 

EX PER. XV.. 

Laftly, in attempting to compound a white by mixing 
the coloured Powders which Painters ufe, I confidered 
that all coloured Powders do fupprefs and flop in 
them a very confiderable part of the Light by which 

they 



[Ill] 

they are illuminated. For they become coloured by 
refledling the Light of their own Colours more copioufly^ 
and that of all other Colours morefparingly, and yet 
they do not refleft the Light of their own Colours fo 
copioufly as white Bodies do. If red Lead/or inftance 
and a white Paper, be placed in the red Light of the 
coloured Spettrum made in a dark Chamber by the re- 
fraction of a Prifm, as is defcribed in the third Eperi-^ 
ment of the firft Book ; the Paper will appear more lu-^ 
cid than the red Lead, and therefore reilefts the red- 
making rays more copioufly than red Lead doth. And 
if they be held in the Light of any other Colour, the 
Light reflected by the Paper will exceed the Light re- 
fieded by the red Lead in a much greater proportion. 
And the like happens in Powders of other ColourSo 
And therefore by mixing fuch Powders we are not to 
exped: a ftrong and full white, fuch as is that of Paper, 
but fome dusky obfcure one, fuch as might arife from a 
mixture of light and darknefs, or from white and black, 
that is, a grey, ordun, orruffetbrown, fuch as are the 
Colours of a Man's Nail, ofaMoufe, of Aflies, of or- 
dinary Stones, of Mortar, of Duft and Dirt in High- 
ways, and the like. And fuch a dark white I have 
often produced by mixing coloured Powders, For thus 
one part of red Lead,and five parts of F^inde ^nsjCom- 
pofed a dun Colour like that of a Moufe. For thefe 
two Colours were feverally fo compounded of others, 
that in both together were a mixture of all Colours j and 
there was lefs red Lead ufed than Viride ^r?^, becaufe 
of the fulnefs of its Colour. Again, one part of red 
Lead, and four parts of blue Bife, compofed a dun Co- 
lour verging a little to purple, and by adding to this a 

certain 



[112] 

certain mixture of Orpiment and Viridi ^ris in a due 
proportion, the mixture loft its purple tindure, and be- 
came perfectly dun. But the Experiment fucceeded beft 
without Minium thus. To Orpiment I added by little 
and little a certain full bright purple, which Painters 
Life until the Orpiment ceafed to be yellow, and became 
ofa pale red. Then 1 diluted that red by adding a 
little Firide Mns.^ and a little more blue Bife than 7A- 
ridl jEris^ until it became of fuch a grey or pale white^ 
as verged to no one of the Colours more than to ano- 
ther. For thus it became of a Colour equal in white- 
neis to that of Afhes or of Wood newly cut, or of a 
Man's Skin. The Orpiment relieved more Light than 
did any other of the Powders, and therefore conduced 
more to the whitenefs of the compounded Colour than . 
they. To affign the proportions accurately may be 
difficult, by reafon of the different goodnefs of Pow- 
ders of the fame kind. Accordingly as the Colour of 
any Powder is m.ore or lefs full and luminous, it ought 
to be ufed in a lefs or greater proportion. 

Now coniidering that thefe grey and dun Colours 
may be alfo produced by mixing whites' and blacks, and 
by confequence ditFer from perfeft whites not in Species 
of Colours but only in degree of luminoufnefs, it is ma- 
nifeft that there is nothing more requilite to make 
them perfeftly white than to increafe their Light fuffi- 
ciently ; and, on the contrary, if by increaiing their 
Liglit they can be brought to perfeft whitenefs, it will 
thence alio follow, that they are of the lame Species of 
-Colour with the beft whites, and differ from them only 
in the quantity of Light. And this I tryed as follows. 
J took the third of the above-mentioned grey mixtures 

(that 



[113] 

f*that which was compounded of Orpiment, Purple, 
Bile and V'lr'de Mrk) and rubbed it thickly upon the 
tloor of my Chamhev, where the Sun fhone upon it 
through the opened Cafement ; and by it, in the flia- 
dow, I laid a piece of white Paper of the fame bignefs. 
Then going from them to the diftance of 11 or 1 8 Feet, 
fo that I could not difcern the unevennefs of the furface 
of the Powder, nor the little (hadows let fall from the 
gritty particles thereof ; the Powder appeared intenfly 
white, fo ^s to tranfcend even the Paper it felf in white- 
nefs, efpecially if the Paper w^re a little Ihaded from 
the Light of the Clouds, and then the Paper compared 
with the Powder appeared of fuch a grey Colour as the 
Powder had done before. But by laying the Paper 
where the Sun ihines through the Glafs of the Window, 
or by fhutting the Window that the Sun might fhine 
through the Glafs upon the Powder, and by fuch other 
fit means of increafing or decreafing the Lights where- 
with the Powder and Paper were illuminated , the 
Light wherewith the Powder is illuminated may be 
made ftronger in fuch a due proportion than the Light 
w^herewith the Paper is illuminated, that they fhall both 
appear exactly alike in whitenefs. For w4ien I was 
trying this, a Friend coming to vifit me, 1 ftopt him 
at the door, and before 1 told him w^hat the Colours 
were, or what I was doing \ I askt him. Which of the 
two whites were the beft, and wherein they diflfered ? 
And after he had at that diftance viewed them well, he 
anfwered. That they were both good whites, and that 
he could not fay which was beft, nor wherein their Co- 
lours differed. Now if you confider, that this white 
of the Powder in the Sun-ftiine was compounded of the 

P Colours 






["41 

Colours which the component Powders ( Orpiment, 
Purple, Bife, and Viride ^ru) have in the fame Sun> 
fliine, you muft acknowledge by this Experiment, as 
well as by the former, that per fed: whitenefs may be 
compounded of Colours. 

From what has been faid it is alfo evident, that the 
whitenefs of the Sun's Light is compounded of all the 
Colours wherewith the feveral forts of rays whereof 
that Light confifts, when by their feveral refrangibili- 
ties they are feparated from one another, do tinge Paper 
©r any other white Body whereon they fall. For thofe 
Colours by Prop. a. are unchangeable, and whenever 
all thofe rays with thofe their Colours are mixt again^ . 
they reproduce the fame white Light as before. . 

PROP. VL PR OB. Ii: 

Jn a mixture of frimary Colours^ the quantity and qualuy 
of each being given j to-. know .the Colony^ of the com--- 
found, 

II , With the Center O and Radius OD defcribe a Circle- 
ADF, anddiftinguiiQiits-circumference into feven parts- 
DE, EF, EG, GA, AB, BC, CD, proportional to 
the feven muiicalTones or Intervals of the eight Sounds^ 
Sol^ la^ fa^ foly /^, mi, fa^ Jol^ contained in an- Eighty 
that is, proportional to the -numbers-^, ;-, 7^? \y 7,, 7^, 
:'. Let the hrft part DE reprefent a red Colour, the 
fecond EF orange, the third EG. yellow,- the fourth 
GH green, the fifth AB blue, the fixth BC indico^ 
and the feventh CD violet. Anch conceive, that thefe 
are all the Colours of uncompoimded. Light gradually 

paffing 



I 



[115 3 

pa fling into one another, as they do when made by 
Frifms ; the circumference DE FG A BCD, reprelen- 
ting the whole leries of Colours from one end of the 
Sun's coloured Image to the other, fo that from D to E 
be all degrees of red, at E the mean Colour between red 
and orange, from E to F all degrees of orange, at F the 
mean between orange and yellow, from F to G all de- 
grees of yellow, and fo on. Let p be the center of 
gravity of the Arch DE, and q, r, s, t, v, x, the centers 
of gravity of the Arches EF, FG, GA, AB, BC 
and CD refpeftively, and about thofe centers of gra- 
vity let Circles proportional to the number of rays of 
each Colour in the given mixture be defcribed; that is, 
the circle p proportional to the number of the red-ma- 
king rays in the mixture, the Circle q proportional to 
the number of the orange-making rays in the mixture, 
and fo of the reft. Find the common center of gravity 
of all thofe Circles p, q, r, s, t, v, x. Let that center 
be Z ; and from the center of the Circle A D F, through 
Z to the circumference, drawing the right line O Y, 
the place of the point Y in the circumference fhall Ihew 
the Colour arifing from the compofition of all the Co- 
lours in the given mixture, and the line OZ fhall be 
proportional to the fulnefs or intenfenefs of the Colour, 
that is, to its diftance from whitenefs. As if Y fall in 
the middle between F and G, the compounded Colour 
Ihall be the beft yellow ; if Y verge from the middle to= 
wards F or G, the compounded Colour fhall according- 
ly be a yellow, verging towards orange or green. If Z 
fall upon the circumference the Colour fliall be intenfe 
and florid inthehigheft degree; if it fall in , the mid 
way between the circumferenceand center, it (hall be 

P 2 ^ but 



[ r 16 ] 

but half fo Intenfe^ that is-, it Ihall be fiich a Colour as 
would be made by diluting the intenfeft yellow with an 
equal quantity of whitenefs ; and if it fall upon the 
center O, the Colour fliall have loft all its intenfenefs^ 
and become a v/hite. But it is to be noted, That if the 
point Z fall in or near the line O D-, the main ingredients 
being the red and violet, the Colour compounded fhall 
not beany of the priimatic Colours, but a purple, in- 
clining to red or violet, accordingly as the point Z 
lieth on the fide of the line D O towards E or towards C^ 
and in general the compounded violet is more bright and 
more fiery than the uncompounded. Alio if only two 
of the primary Colours which in the Circle are oppofite 
to one another be mixed in an equal proportion, the 
point Z (hall fall upon the center O, and yet the Co- 
lour compounded of thofe two ihall not be perfectly 
white, but Ibme faint anonymous Colour. For I could 
never yet by mixing only two primary Colours produce 
a perfect white. Whether it may be compounded of a 
mixture of three taken at equal difliances in the circum- 
ference I do not know, but of four or five 1 do not much 
cjueftion but it may. But thefe are curiofities of little 
or no moment to the underftanding the Phenomena of 
nature. For in all whites produced by nature, there 
nfes to be a mixture of all forts of rays, and by confe- 
quence a compofition of aU Colours. 

To give an initance of this Rule ; fuppofe a Colour is 
compounded of thefe homogeneal Colours, of violet 
1 part, of indico i part, of blue 2 parts, of green 3 parts^ 
of yellow 5 parts, of orange 6 parts, and of red iq parts. 
Proportional to thefe parts I defcribe the Circles x, v, t, 
h r, q, p refpeftively, that is^ fo that if the Circle x 

be 



I 



[117] 

be I, the Circle v may be i, the Circle t 2, the Circle 
s ^, and the Circles r, qandp, 5, 6 and 10. Then I 
find Z the common center of gravity of thefe Circles, 
and through Z drawing the line O Y^ the point Y falls 
upon the circumference between E and F, fome thino- 
nearer to E than to F, and thence I conclude^ that the 
Colour compounded of thefe ingredients will be an 
orange^ verging a little more to red than to yellow. 
Alfo I find that O Z is a little lefs than one half of 
OY, and thence I conclude, that this orange hath a 
little lefs than half the fulnefs or intenfenefs of an un- 
compounded orange ; tte,t is to fay, that it is fuch an^ 
orange as may be made by mixing an homogeneal orange 
Vvdth a good white in the proportion of the line OZ to 
the line Z Y, this proportion being not of the quantities 
of mixed orange and white powders, but of the quan- 
tities of the lights reiieSed from them. 

This Rule I conceive accurate enough for pradife^. 
though not mathematically accurate ; and the truth of 
it may be fufficiently proved to fenfe, by flopping any 
of the Colours at the Lens in the tenth Experiment of 
this Book. For the reft of the Colours which are riot 
flopped, but pafs on to the Focus of the Lens, will' 
there compound either accurately or very nearly fuch 
a Colour as by this Rule ought to rcfult from, their 
mixture^ 



PRO P^ 



[liS] 



PROP. VIL THEOR. V. 

^^4U the Colours in the Univerje 'Ui)htch are made l^ L'ght^^ 
and defend not on the jpower of imagination^ are 
either the Colours of homogeneal Lights^ or com founded 
of thefe and that either accurately or ver'j nearl'j^ ac* 
wording to the Bjule of the foregoingTroMem. ^ 

For it has been proved ( in Prop. i. Lii.^.) that the 
changes of Colours made by refractions do not arife 
from any new modifications of the rays impreft bj/ thofe 
refractions^ and by the various terminations of Hght 
andfhadow, as has been the conftant and general opi- 
nion of Philofophers. It has alfo been proved that the 
leveral Colours of the homogeneal rays do conftantly 
anfwerto theu' degrees ofrefrangibility, (Prop, i . L^z^. i . 
and Prop.::. L^'/^.'^.J and that their degrees of refrangi^ 
bility cannot be changed by refractions and reflexions^ 
(Prop.i.X^/^.i.j and by confequence that thofe their 
Colours are likewdfe immiutable. It has alfo been pro- 
ved direjftly by refraCiing and reflecting homogeneal 
Lights apart, that their Colours .cannot be changed^ 
(Prop.!. Lib,''^.) It ^has been proved alfo, that wdien 
the feveral forts of rays are mixed, and in croffing pafs 
through the lame fpace, they do not aCt on one another 
ib as to change each others colorifick qualities, (Exper. 
io.Lii.'2.) but by mixing their aCtions in the Senfo- 
rium beget a fenfation differing from what either would 
do apart, that is a fenfation of a mean Colour between 
their proper Colours ; and particularly when by the 
jQoncourfe and mixtures of all forts of rays, a white 

Colour 



[up] 

Colour is produced, the white is a mixture of all the 
Colours which the rays would have apart, ( Prop, 5. 
Ltk a. J The rays in that mixture do not lofe or alter 
their feveral colorifick qualities, but by all their various 
kinds of adions mixt in the Senforium, beget a fenia- 
tion of a middling Colour between all their Colours 
which is whitenefs. For whitenefs is a mean between 
all Colours, having it felf indifferently to themall^ fo 
as with equal facility to be tinged with any of them; 
A red Powder mixed with a little blue, or a blue- with 
a little red, doth not prefently lofe its Colour, but a 
white Powder mixed with any Colour is prefently tin- 
ged with that Colour, and is equally capable of beinc? 
tinged with any Colour what-ever. It has been Ihewed 
aifo, that as the Sun's Light is mixed of all forts of rays, 
fo its whitenefs is a mixture of the Colours of all forts 
of rays ; thofe rays having from the beginning their fe- 
veraL colorific qualities as wallas their ieveral refrangi-' 
bilities, and retaining them perpetually unchanged not^ 
withftanding any refractions or reflexions they m.ay at 
any time fuffer, and that when-ever any fort of the 
Sun's rays is by any means (as by reflexion in Exper. 9- 
and io. LtL i. or by refraftion as happens in all re-' 
fraftions ) fepa rated from the reft, they then- manifeit 
theirproper Colours, Thefe things have been proved,' 
and thefum. of all this amounts to the Prapoiition here 
to be proved>:. Eor if the Sun's Light is mixed of fe- 
veral forts of rays, each of which have originally their . 
feveral refrangibilities and colorifick quilities, and not- 
withftanding their refraftions and refleftions, and their 
various feparations or mixtures, keep thofe their ori- 
ginal properties perpetually. the fame without altera- 
tion : 



■*^'^' "^ 



[ 120] 
^tion ) fiien all the Colours in the World muft be fuch as 
conftantly ought to arife from the original colorific qua- 
lities of the rays whereof the Lights confift by which 
thofe Colours are feen. And therefore if thereafon of 
any Colour what-ever be required, we have nothing elfe 
to do then to confider how the rays in the Sun's Light 
have by reflexions or refraftions, or other caufes been par- 
ted from one another^or mixed together j or otherwiie to 
find out what forts of rays are in the Light by which 
that Colour is made, and in what proportion; and 
then by the laft Problem to learn the Colour which 
ought to arife by mixing thofe rays (or their Colours) 
in that proportion. I fpeak here of Colours fo far as 
they arife from Light. For they appear fometimes by 
other caufes, as when by the power of phantafy we 
fee Colours in a Dream, or a mad Man fees things before 
him which are not there i or when we fee Fire by ftriking 
the Eye, or fee Colours like the Eye of a. Peacock's 
Feather, by prefiing our Eyes in either corner whilft 
we look the other way. Where thefe and fuch like 
caufes interpofe not, the Colour always anfwers to 
the fort or forts of the rays whereof the Light confifts, 
as I have conftantly found in what^ever Phenomena of 
Colours I have hitherto been able to examin, I fliall in 
the following Propofitions give inftances of this in the 
.Jh^nomena of chiefeft note. 



PROP. 



PROP. VIIL PROB. III. 

Bi the dijcovered Troperties of Light to explain the 
Colours ynade b^ Prijms. 

Let ABC reprefent a Prifm refracting the Light of p^o-. xi. 
the Sun, which comes into a dark Chamber through a 
Hole F <? almoft as broad as the Prifm, and let M N 
reprefent a white Paper on which the refracted Light is 
caft, and fuppofe the moft refrangible^or deepeft violet 
making rays fall upon the fpace P-tt , the leaft refran- 
gible or deepeft red-making rays upon the fpace Ti, 
the middle fort between the Indico-making aud blue- 
making rays upon the fpace d^ , the middle fort of the 
green-making rays upon the fpaceRe, the middle fort 
between the yellow-making and orange-making rays 
upon the fpace S<T? and other intermediate forts upon 
intermediate fpaces. For fo the fpaces upon which the 
feveral forts adequately fall will by reafon of the diffe- 
rent refrangibility of thofe forts be one lower than ano- 
ther. Now if the Paper MN be fo near the Prifm that the 
fpaces P T and ttT do not interfere with one another, the 
diftance between them T TT will be illuminated by all 
the forts of rays in that proportion to one another which 
they have at their very firft coming out of the Prifm^ 
and confequently be white. But the fpaces PT and ^^ 
on either hand, will not be illuminated by them all, 
and therefore will appear coloured. And particularly 
at P, where the outmoft violet-making rays fall alone., 
the Colour muft be the deepeft violet. At Q. where the 
violet-makino; and indico-makinp; rays are mixed ^ it 

Q muft 



[ 122] 

nnift be a violet inclining much to indico. At R where 
the violet-making , indico-making, blue-making, and 
one half of the green-making rays are mixed, their Co- 
lours muft ( by the conftruftion of the fecond Problem) 
compound a middle Colour between indico and blue. 
At S where all the rays are mixed except the red-ma- 
king and orange-making,their Colours ought by the fame 
Rule to compound a faint blue, verging more to green 
than indie. And in the progrefs from S to T, this blue 
will grow more and more faint and dilute, till atT^ 
where all the Colours begin to be mixed , it end iji 
whitenefs. 

So again, t)n the other fide of the white at T, w^here 
the leaft refrangible or utmxoft red-making ^ays are alone 
the Colour muft be the deepeft red. At cr the mixture 
of red and orange will compound a red inclining ta 
orange. At e the mixture of red, orange, yellow, and 
one half of the green muft compound a middle Colour 
between orange and yellow. At x the mixture of all 
Colours but violet and indico will compound a faint 
yellow, verging more to green than to orange. And 
this yellow will grow more faint and dilute continually 
in its progrefs from y^ to tt, where by a mixture of ail 
forts of rays it will become white. 

Thefe Colours ought to appear were the Sun's Light 
perfectly white: But becaufe it inclines to yellow,theex- 
cefs of the yellow-making rays whereby 'tis tinged with, 
that Colour, being mixed with the faint blue between. 
S and T, will draw it to a faint green. And fo. the 
Colours in order from P to T ought to be violet, indico, 
blue, very faint green, white, faint yellow, orange, red. 
Thus it is by the computation : And they that pleafe to,. 

view 



[123] 

view the Colours made by a Prifm will find it fo in 
Nature. 

Thele are the Colours on both fides the white when 
the Paper is held between the Prifm, and the point X 
where the Colours meet, and the interjacent white va- 
nifhes. For if the Paper be held ftill farther off from the 
Prifm, the moft refrangible and leaft refrangible rays 
will be wanting in the middle of the Light, and the reft 
ofthe rays which are found there, will by mixture pro- 
duce a fuller green than before. Alfo the yellow and 
blue will now become lefs compounded, and by con- 
fequence more intenfe than before. And this alfo 
agrees with experience. 

And if one look through a Prifm upon a white Objed 
encompafled with blacknefs or darknefs, the reafon of 
the Colours arifing on the edges is much the fame, as 
will appear to one that (hall a little confider it. If a 
black Objeft be encompaffed with a white one, the Co- 
lours which appear through the Prifm are to be derived 
from the Light of the white one, fpreading into the Re* 
gions of the black, and therefore they appear in a con* 
trary order to that, in which they appear when a white 
Objeft is furrounded with black. And the fame is to 
be underftood when an Objed is viewed, whofe parts 
are fome of them lefs luminous than others. For in the 
Borders of the more and lefs luminous parts, Colours 
ought always by the fame Principles to arife from the 
excefs ofthe Light ofthe more luminous, and to be of 
the fame kind as if the darker parts were blacky but yet 
to be more faint and dilute. 

'0.2 What 



[124] 

What is faid of Colours made by Prifms may be eafily 
applied to Colours made by the Glafles of TelefeopeSj^ 
or Microfcopes, or by the humours of the Eye. For if 
the Objedl'glafs of a Telefcope be thicker on one fide 
than on the other^ or if one half of the Glafs, or one 
half of the Pupil of the Eye be covered with any opake 
fubftance : the Objed-glafs, or that part of it or of the 
Eye which is not covered, may be confidered as a Wedge 
with crooked fides, and every Wedge of Glafs^ or other- 
pellucid fubftaace, has the effed of a Prifm in refrading 
the Light which paflTes through it. 

How the Colours in the 9th and loth Experiments 
of the firft Part arife from the different reflexibility of 
Lightjis evident by what was there faid. But it is obfer- 
vable in the 9tii Experiment, that whilft the Sun's di- 
red Light is yellow, the excefs of the blue-making 
rays in the refleded Beam of Light MN, fuffices only; 
to bring that yellow to a pale white inclining to blue^. 
and not to tinge it with a manifefl:ly blue Colour. To 
obtain therefore a better blue, I ufed inftead of the yel- 
low Light of the Sun the white Light of the Clouds, by., 
varying a little the Experiment as follows^. 

EX PER. XVL 

15. Let H F G reprefent a Prifm in the open Air, and S 
the Eye of the Spedator, viewing the Clouds by their. 
Light coming into the Prifm at the plane fide F IG K^ 
and refleded in it by its bafe H E I G, and thence going 
out through its plain fide HEFK to the Eye. And 
when the Prifm and Eye are conveniently placed, fo 
that the Angles of incidence and reflexion at the bafe 

may 



[125] 

may be about 40 degrees^ the Spectator will fee a Bow^ 
MN of a blue Colour, running irom one end of the. 
bafe to the other, with the concave fide towards him,, 
and the part of the bafe IMNG beyond this Bow will 
be brighter than the other part EMNH on the other 
fide ol it. This blue Colour MN being made by no- 
thing elfe than by reflexion of a fpecular iuperficies^ 
leems fo odd a Ph^nomienon, and fo unaccountable for • 
by the vulgar Hypothefis of Philofophers, that I could 
not but think it deferved to be taken notice of. Now 
for underftanding the reafon of it, fuppofe the plane/ 
ABC to cut the plane fides and bafe of the Prifm per- ^ 
pendicularly. From the Eye to the line BC, wherein that 
plane cuts the bafe, draw the lines S p and S t^ in the - 
Angles Spc 50 degr. ;, andStc49 degr.-^g, and the. 
point p will be the limit beyond which none of the moft./ 
refrangible rays can pafs through the bafe of the Prifm, 
and be refradted, whofe incidence is fuch that they may 
be refleded to the Eye ; and the point t wdll be the like 
limit for the ieaft refrangible rays, that is, beyond 
which none of them can pafs through the bafe, whofe : 
incidence is fuch that by reflexion they may come to the? 
Eye. And the point r taken in the middle vv^ay between 
p and t, will be the like limit for the meanly refrangible 
rays. And therefore all the refrangible rays which fall 
upon the bafe beyond t, that i;s, between t and B, and. 
can come from thence to the Eye will be reflefted thi- 
ther : But on this fide t, that is, between t and c, many, 
of thefe rays will be tranfmitted through the bafe. , 
And all the moil: refrangible rays which fall upon the. 
bafe beyond p, that is , between p and B, and can by 
r^eiiexion come from thence to the Eye, will be reflected/ 

thither^. 



[ I^^ ] 

thither, but every where between t and c, many of 
thefe'rays will get through the bafe and be refrafted; 
and the fame is to be underftood of the m.eanly refran- 
gible rays on either fide of the point r. Whence it fol- 
lows, that the bafe of the Prifm muft every vv^here be- 
tween t and B, by a total reflexion of all forts of rays to 
the Ey^, look white and bright. And every where 
between/ andC, byreafon ofthe tranfmiffion ofmany 
Tays of every fort, look more pale, obfcure and dark. 
But at r, and in other places between p and t, where 
all the more refrangible rays are reflefted to the Eye, 
and many of the lefs refrangible are tranfmitted, the 
-excefs ofthe mod refrangible in the refleded Light will 
tinge that Light with their Colour, which is violet and 
blue. And this happens by taking the line CprtB any 
where between the ends ofthe Prifm H G and EI. 

PROP. IX. PROB. IV. 

■'By the dijcovered Troferties of Light to e,x^lain the 
Colours of the Rjim^h'w. 

This -Bow never appears but where it Rains in the 
Sun-fhine, and may be made artificially by fpouting up 
Water which may break aloft, and fcatter into Drops, 
and faH<lown like Rain. For the Sun Ihining upon thefe 
Drops certainly caufes the Bow to appear to a Speda- 
Cor itanding in a due pofition to the Ram and Sun. And 
hence it is now^ agreed upon, that this Bow is made by 
refradion of the Sun's Light in Drops of falling Rain. 
This was underftood by fome of the Ancients, and of 
late more folly difcovered and explained by the Famous 

j4ntonit^ 



C 127 ] 

\Ayitonim de ^miinis Archbilhop of SfilatOy in his Boole. 
"De Radiis Vift^ if)' L?4as^ publifhed by his Friend Bar^ 
tolm at I^enice^ in the Year 161 1, and written above 
twenty Years before. For he teaches there how the 
interior Bow is made in round Drops of Rain by two 
refradlions of the Sun's Light, and one reflexion be- 
tween them, and the exterior by two refraftions and 
two forts of reflexions between them in each Drop of 
Water 5 and proves his Explications by Experiments 
made with a Phial full ofWater^and with Globes of Glais 
filled with W^er, and placed in the Sun to make the 
Colours of the two Bows appear in them. The fame 
Explication ^es^Cartes hath purfued in his Meteors, 
and mended that of the exterior Bow. But whilft they 
underftood not the true origin of Colours, it's neceffary 
to purfue it here a little further. For underfl:anding 
therefore how the Bow is made, let a Drop of Rain or 
any other fpherical tranfparent Body be reprefented by 
the Sphere B N F G, defcribed with the Center C, and F%. i 
Semi-diameter CN. And let AN be one of the Sun's 
rays incident upon it at N, and thence refraft^ed to F, , 
wliere let it either go out of the Sphere by refraSion to- 
wards V, or be reflected to G ;, and at G let it either go^ 
out by refraction to R, or be reflected to H ; and. at H 
let it go out by refradtion towards S, cutting the inci- 
dent ray in Y j,; produce AN and RG, till they meet in 
X, and upon A X and N F let fall the perpendiculars 
CD and CE, and produce CD till it fall upon the cir- 
cumference at L. Parallel to the incident ray AN draw, 
the Diameter B Q, and let the fine of incidence out of 
Air into Water be to the fine of refraftion as- 1 to. 
R. Now if you fuppofe the point of incidence N to- 

move 



.[128] 

move from the point B, continually till It come to L, 
the Arch QF will firft increafe and then decrcafe, and 
lb will the Angle AXR which the rays AN and GR 
contain ; and the Arch Q F and Angle AXR will be 
biggeit when ND is to CN as a^iiIrr to //^ RR, 
in which cafe N E will be to N D as a R to I. Alfo the 
Angle AYS which the rays A N and HS contain will 
firft decreafe, and then increafe and grow leaft when 
ND is to CN as /^II-RR to//8 RR, in which cafe 
N E will be to N D as 3 R to I. And fo the Angle which 
the qext emergent ray ( that is, the emergent ray after 
three reflexions ) contains with the incident ray AN 
will come to its limit whenND is to CN as i/ \\.-^^ to 
7/15 RR, in which cafe N E will be to ND as 4.R to I, 
and the Angle which the ray next after that emergent, 
that is, the ray emergent after four reflexions, con- 
tains with the incident will come to its limit^ when 
ND is to C N/ as /^ii-RR to /ij^ RR , in which cafe 
N E will be to N D as 5 R to Y\ and fo on infinitely, 
the numbers 5, 8, 15^ ^4., )Bc\ being gathered by conti- 
nual addition of the terms of the arithmetical progreflion 
3, 5,7,9,}5)'<r. The truth of all this Mathematicians will 
eafily examine. >TtW.i»>^/A i^. ^^z^^"?^/. /^ -^^z 

Now it is to be obferved^ that as w^hen the Sun comes 
to his Tropicks, days increafe and decreafe but a very 
little for a great v/hile together ; fo when by increaf ng 
the diftance C D, thefe Angles come to their limits, 
they vary their quantity but very little for fome time 
together, and therefore a far greater number of the rays 
which fall upon all the points N in the Quadrant 
B L , fhall emerge in the limiits of thefe Angles , 
tJien in any other inclinations. And further it is 

to 



[129] 

to be obierved, that the rays which differ in refrangi- 
bility will have different limits of their Angles of emer- 
gence, and by confequence according tcftheir different 
degrees of refrangibility emerge, moff copioufly in dif- 
ferent Angles, and being feparated from one another 
appear each in their proper Colours. And what thofe 
Angles are may be eafily gathered from the foregoing 
Theorem by computation. 

For in the leaft refrangible rays the fines I and R (as 
was found above) are io8 and 8i, and thence by 
computation the greateft Angle A X R will be found 
42 degrees and a minutes, and the leaft Angle AYS, 
50 degr. and 57 minutes. And in the moft refrangible 
rays the fines I andR are 109 and 81, and thence by 
computation the greateft Angle AX R will be found 
4.0 degrees and 17 minutes, and the leaft Angle AYS 
54. degrees and 7 minutes. 

Suppofe now that O is the Spectator's Eye, and OP a line pig, 1 5 . 
drawn parallel to the Sun's rays, and let P O E, P O F, 
POG, POH, be Angles of 40 degr. i7min. 41 degn 
0, min. 5odegi. 57 min. and 54 degr. 7 min. refped:ively, 
and thefe Angles turned about their common fide O P5 
(hall with their other fides OE, OF; OG, OH de- 
defcribe the verges of two* Rain-bows A F B E and 
CHDG. For if E, F, G, H, be Drops placed any 
where in the conical fuperficies defcribed by O E, O F, 
OG, OH, and be illuminated by the Sun's rays SE, 
SF, SG, SH; the Angle SEO being equal to the 
Angle POE or 40 degr. 17 min. ftiali be the greateft 
Angle in which the moft refrangible rays can after one 
reflexion be refraded to the Eye, and therefore all the 
Drops in the line O E fhall fend the moft refrangible 

R rays 



[ ISO ] 

rays moft copioudy to the Eye, and thereby ftrike the 
lenfes with tli£ deepefl: violet Colour in that region. 
And in like manner the Angle SFO being equal to 
the Angle P OF, or 4.1 deg. 2 min. fhall be the greatefi: 
in which the leaft refrangible rays after one reflexion 
can emerge out of the Drops, and therefore thofe rays 
fhall come moft copioufly to the Eye from the Drops in 
the line O F, and ftrike the fenfes with the deepeft red 
Colour in that region. And by the fame argument,, 
the rays which have intermediate degrees of refrangibi- 
lity fhall come moft copioufly from Drops between 
E and F, and ftrike the fenfes with the intermedi;ite 
Colours in the order which their degrees of refrangibi- 
lity require, that is, in the progrefs from E to F, or 
from the iniide of the Bow to the outhde in this order^ 
violet, indico, blue, green, yellow,orange, red. But the 
violet, by the mixture of the white Light of the Clouds, 
will appear faint and incline to purple. 

Again, the Angle S G O being equal to Angle P O G, 
or 50 gr. 51 min. fhall be the leaft Angle in which the 
leaft refrangible rays can after two reflexions emerge out 
oftheDrops,and therefore the leaft refrangible rays fhall 
come moft copioufly to the Eye from the Drops in the 
line O G, and ftrike the fenfe with the deepeft red in 
that region. And the Angle S HO being equal to the 
Angle POH or 54. gr. 7 min. fhall be the leaft Angle in 
which the moft refrangible rays after two refledions can 
emerge out of the Drops, and therefore thofe rays fliall 
come moft copioufly to the Eye from the Drops in the 
line O H, and ftrike the fenfes with the deepeft violet in 
that region. And by the fame argument, the Drops in 
the regions between G and H fliall ftrike the fenfe with 

the 



the Intermediate Colours in the order which their de> 
grees of refrangibility require, that is, in the prooTefs 
from G to H, or from the infide of the Bow to the out- 
iide in this order^ red, orange, yellow, green, blue, in- 
dico, violet. And fmce theie four lines O E, O F, O G. 
O H, may be fituated any where in the above-mentioned 
conical fuperficies, what is faid of the Drops and Co- 
lours in thefe lines is to be underftood of the Drops 
and Colours every where in thofe fuperficies. 

Thus fhall there be made two Bows of Colours, an 
interior and ftronger, by one reflexion in the Drops, 
and an exterior and fainter by two j for the Light be- 
comes fainter by every reflexion. And their Colours 
iliall ly in a contrary order to one another, the red of 
both Bows bordering upon the fpace G F which is be- 
tween the Bows. The breadth of the interior Bow 
EOF meafured crofs the Colours fliall be i degr. 45 min. 
and the breadth of the exterior GOH fliall be 3 
degr. 10 min. and the diftance between them GOF 
(hall be 8gr. 55 min. the greatefl: Semi-diameter of the 
innermufl:, that is, the Angle POF being 4a gr. 1 min. 
and the leaft Semi-diameter of the outermofl P O G, be- 
ing 50 gr. 57 min. Thefe are the meafures of the Bows, 
as they would be were the Sun but a point ; for by the 
breadth of his Body the breadth of the Bows will be in- 
ereafed and their diftance decreafed by half a degreej 
and fo the breadth of the interior Iris will be 1 degn 
1 5 mm. that of the exterior 3 degr, 40 min. their di- 
ftance 8 degr, a 5 min. the greateft Semi-diameter of the 
interior Bow 4adggr. 17 min. and the leaft of the ex» 
terior 50 degn 4^ min. And fiich .are, the dimenfions 
of the Bows in the Heavens found to be very nearly, 

R a when 



[132] 

when their Colours appear ftrong and perfed:. For 
once, by inch means as I then had, I meafured the 
greateft Semi-diameter of the interior Iris about 4.2 de- 
grees, the breadth of the red, yellow and green in that 
Iris 63 or 64. minutes, befides the outmoft faint red ob- 
fcured by brightnefs of the Clouds, for which we 
may allow 3 or 4. minutes more. The breadth of the 
blue was about 40 minutes more befides the violet, 
which was fo much obfcured by the brightnefs of the 
Clouds, that I could not meafure its breadth. But 
luppofing the breadth of the blue and violet together 
to equal that of the red, yellow and green together, the 
whole breadth of this Iris will be about 1^ degrees as 
above. The leaft diftance between this Iris and the ex- 
terior Iris was about 8 degrees and go minutes. The ex- 
terior Iris was broader than the interior, but fo faint^ 
efpecially on the blue fide, that I could not meafure its 
breadth diftinftly. At another time when both Bows 
appeared more diftindl:, I meafured the breadth of the 
interior Iris a gr. ic, and the breadth of the red, yel- 
low and green in the exterior Iris, was to the breadth 
of the fame Colours in the interior as g to a. 

This Explication of the Rain-bow is yet further con- 
firmed by the known Experiment ( m.ade by y^ntoni'us 
de T)ominis and "Des^Cartes) of hanging^ up any where 
in the Sun-lliine a Glafs-Globe filled with Water, and 
viewing it in fuch a pofl:ure that the rays which come 
from the Globe to the Eye may contain with the Sun's 
rays an Angle of either 4^ or 50 degrees. For if the 
Angle be about 42 or 43 degrees, the Spectator ( fup- 
pofe at O) fliall fee a full red Colour in that fide of the 
Globe oppofed to the Sun as 'tis reprefented at F, and 

if 



[133] 

if that Angle become lefs ( luppole by depreffing the 
Globe to E ) there will appear other Colours^ yellow, 
green and blue fucceffively in the lame fide of the Globe, 
But if the Angle be made about 50 degrees (luppole by 
lifting up the Globe to G)there will appear a red Colour 
in that fide of the Globe towards the Sun, and if the 
Angle be made greater (fuppole by lifting up the Globe 
to H) the red will turn fucceffively to the other Colours 
yellow, green and blue. The fame thing I have tried by 
letting a Globe reft, and railing or depreffing the Eye, 
or otherwife moving it to make the Angle of a juft 
magnitude. 

I have heard it reprefented,. that if the Light of a 
Candle be refraSed by a Prifm to the Eye ; when the 
blue Colour falls upon the Eye the Spefilator lliall fee 
red in the Prifm, and when the red falls upon the Eye 
he Ihallfee blue ; and if this were certain, the Colours 
of the Globe and Rain-bow ought to appear in a con- 
trary order to w^hat we find. But the Colours of the 
Candle being very faint, the miftake feems to arife from 
the difficulty of difcerning what Colours fall on the 
Eye. For, on the contrary, I have fometimes had oc- 
cafion to obferve in the Sun's Light refraded by a Prifm, 
that the Spectator always fees that Colour in the Prifm 
which falls upon his Eye. And the fame I have found 
true alfo in Candle-Light. For when the Prifm is mo- 
ved llowly from the line which is drawn direftly from the 
Candle to the Eye,the red appears firft in the Prifm, and 
then the blue, and therefore each of them is feen when^ 
it falls upon the Eye. For the red pafTes over the Eye 
firft, and then the blue. 

The 



[134-3 

The Light which, comes through Drops of Rain by 
two refradions without any reflexion, ought to appear 
ftrongeft at the diftance of about a 6 degrees from the 
Sun, and to decay gradually both ways as the diftance 
from him increafes and decreafes. And the fame is to 
be underftood of Light tranfmitted through fpherical 
Hail-ftones. And if the Hail be a little flatted, as it 
often is, the Light tranfmitted may grow fo ftrong at 
a little lefs diftance than that of a 6 degrees, as to form 
a Halo about the Sun or Moon ; w4iich Halo, as often 
as the Hail-ftones are duly figured may be coloured, 
and then it muft be red within by the leaft refrangible 
rays,and blue without by the moft refrangible ones,efpe- 
daily if the Hail-ftones have opake Globules of Snow in 
their center to intercept the Light within the Halo ( as 
Htigenins has obferved) and make the infide thereof more 
diftinflly defined than it would otherwife be. For 
fuch Hail-ftones, though fpherical, by terminating the 
Light by the Snow, may make a Halo red within and 
colourlefs without, and darker in the red than with- 
out, as Halos ufe to be. For of thofe rays which pais 
clofe by the Snow the rubriform will be leaft refradted^^ 
and fo come to the Eye in the diredeft lines. 

The Light which paffes through a Drop of rain after 
two refractions, and three or- more reflexions, is fcarce 
ftrons enough to^ caule a feniible Bow^ ; but in thofe Cy- 
Hnders of Ice by w^iich Hug^nm explains the TarkeUa^ 
it may perhaps be fenfible. 



PROP. 



[135 J 

P R O p. X. P R O B. V. 

Bi the difcovered "properties of Light to explain the per-^ 
manent Colours of natural Bodies, 

Thefe Colours arife from hence, that fome natural 
Bodies relied fome forts of rays, others other forts more 
copiouily than the reft^ Minium reflets the leafl: re- 
frangible or red-making rays moft copioufly, and thence 
appears red. Violets reflect the moft refrangible, moft 
copioufly, and thence have their Colour, and fo of other 
Bodies. Every Body reflects the rays of its own Colour 
more copiouily than the reft, and from their excefs and 
predominance in the reflected Light has its Colour. 

EX PER. XVII. 

For if the homogeneal Lights obtained by the folu- 
tion of the Problem propofed in the 4.th Propofition of 
the lirftBook you place Bodies, of feveral Colours, you 
will find, as I have done, that every Body looks moft 
fplendid and luminous in the Light of its ov^n Colour. 
Cinnaber in the homogeneal red Light is moft refplen- 
dent, in the green Light it is manifeftly lefs refplen- 
dent, and in the blue Light ftill lefs. Indico in the 
violet blue Light is mioft refplendent, and its fplendor 
is gradually diminiftied as it is removed thence by de- 
grees through the green and yellow Light to the red. 
By a Leek the green Light, and next that the blue and 
yellow which compound green, are more ftrongly re- 

fleded 



fleded than the other Colours red and violet^and fo of the 
reft. But to make thefe Experiments the more manifeft, 
fuch Bodies ought to be chofen as have the fulleft and 
moft vivid Colours, and two of thofe Bodies are to be 
compared together. Thus, for inftance, if Cinnaber 
Ca^Y^urrr Cyp^'u^ and ultrci marine blue , or fome other full blue be 
^d .^Z...^^— -j^^j^ t^S^etherln^e homogeneal Light, they will both 
appear red, but the Cinnaber will appear of a ftrongly 
luminous and refplendent red, and the ultra marine 
blue of a faint obfcure and dark red^; afid if they be 
held together in the blue homogeneal Light they will 
both appear blue, but the ultra marine will appear of 
a ftrongly luminous and refpleij^^ent blue, and the 
Cinnaber of a faint and dark blue^ "'Which puts it out 
of difpute , that the Cinnaber reflefts the red Light 
much more copioully than the ultra marine doth, and 
the ultra marine retlefts the blue Light much more co- 
pioufly than the Cinnaber doth. The fame Experiment 
may be tryed fuccesfuUy with red Lead and Indico, or 
with any other two coloured Bodies, if due allowance 
be made for the different ftrength or weaknefs of their 
Colour and Light. 

And as the reafon of the Colours of natural Bodies is 
evident by thefe Experimenrs, fo it is further confirmed 
and put paft difpute by the two firft Experiments of the 
firft Book, whereby 'twas proved in fuch Bodies that 
the reflefted Light which differ in Colours do differ alfo 
in degrees of refrangibility. For thence it's certain, 
that fome Bodies retied the more refrangible, others 
the lefs refrangible rays more copioufly. 

And 



[i37] 

And that this is not only a true reafon of thefe Co- 
lours, but even the only reafon may appear further 
iroiii this confideration, that the Colour of homogeneal 
Light cannot be changed by the reflexion of natural 
Bodies. 

For if Bodies by reflexion cannot in the leaft change 
the Colour of any one fort of rays, they cannot appear 
coloured by any other means than by refleding thofe 
which either are of their own Colour, or which by 
mixture mufl: produce it. 

But in trying Experiments of this kind care muft be 
had that the Light be fufficlently homogeneal. For if 
Bodies be illuminated by the ordinary prifmatick Co- 
lours, they will appear neither of their own day-light 
Colours, nor of the Colour of the Light cafl: on them, 
but of fome middle Colour between both, as I have 
found by Experience. Thus red Lead ( for inftance ) 
illuminated with the ordinary prifmatick green will 
not appear either red or green, but orange or yellow, 
or between yellow and green accordingly, as the green 
Light by which "'tis' illuminated is more or lefs com- 
pounded. For becaufe red Lead appears red when il- 
luminated with white Light, wherein all forts of rays 
are equally mixed, and in the green Light all forts of 
rays are not equally mixed, the excefs of the yellow- 
making, green-making and blue-making rays in the 
incident green Light, will caufe thofe rays to abound 
fo m.uch in the reflefted Light as to draw the Colour 
from red towards their Colour. And becaufe the red 
Lead refleds the red-making rays moft copioufly in 
proportion to their number, and next after them the 
orange-making and yellow-making rays ; thefe rays in 

S the 



the reflefted Light will be more in proportion to the 
Light than they were in the incident green Light, and 
thereby will draw the refleded Light from green to- 
wards their Colour. And therefore the red Lead will ap- 
pear neither red nor green ^but of a Colour between both. 
In tranfparently coloured Liquors 'tis oblervable, 
that their Colour ufes to vary with their thicknefs. 
Thus, for inftance, a red Liquor in a conical Glafs 
held between the Light and the Eye, looks of a pale 
and dilute yellow at the bottom where 'tis thin, and a 
little higher where 'tis thicker grows orange,and where 
'tis ftill thicker becomes red, and where 'tis thickeft 
the red is deepeft and darkeft. For it is to be conceived 
that fuch a Liquor ftops the indico-making and violet- 
making rays moft eafily, the blue- making rays more 
difficultly, the green^making rays ftill more difficultly, 
and the red-making moft difficultly : And that if the 
thicknefs of the Liquor be only fo much as fuffices to 
ftop a competent number of the violet-making and in- 
dico-making rays, without diminilhing much the num- 
ber of the reft, the reft muft ( by Prop. 6. TJib, i.) com- 
pound a pale yellow. But if the Liquor be fo much 
thicker as to ftop alfo a great number of the blue-making 
rays, and Ibme of the green-making, the reft muft com- 
pound an orange ; and w^here it is fo thick as to ftop 
alfo a great number of the green-making and a confi- 
derable number of the yellow-making, the reft muft 
begin to compound a red, and this red muft grow deeper 
and darker as the yellow making and orange-making 
rays are more and more ftopt by increaiing the thick- 
nefs of the Liquor, fo that few rays beiides the red- 
making can get through. . ^ 

^ Of 



[ 1 3P ] 

Of this kind Is an Experiment lately related to me by 
- Mr. Halle^j^ who, in diving deep into the Sea, found 
in a clear Sun-(hine day, that when he was funk many 
Fathoms deep into the Water, the upper part of his 
Hand in which the Sun fhone diredly through the 
Water looked of a red Colour, and the under part of 
his Hand illuminated by Light reHe£ted from the Water 
below looked green. For thence it, may be gathered, 
that the Sea -water reflects back the violet and blue- 
making rays moft ealily, and lets the red-making rays 
pafs moft freely and copioully to great depths. For 
thereby the Sun's dire£t Light at all great depths, by 
reafon of the predominating red-making rays, muft 
appear red; and the greater the depth is, the fuller 
and intenfer muft that red be. And at fuch depths as 
the violet-making rays fcarce penetrate unto, the blue- 
making, greei)-m.aking and yellow-making rays being 
reflected from below iti ore copioully than the red-making 
ones, muft compound a green. 

Now if there be two Liquors of full Colours, fup- 
pofe a red and a blue, and both of them fo thick as 
iuffices to make their Colours fufficiently full ; though 
either Liquor be fufficiently tranfparent apart, yet 
will you not be able to fee through both together. For 
if only the red-making rays pafs through one Liquor^ 
and only the blue-making through the other, no rays 
can pafs through both« This Mr. Hook tried cafually 
with Glafs-wedges filled with red and blue Liquors^ 
and was furprized at the unexpected event, the reafon 
of it being then unknown ; which makes me truft the 
more to his Experiment, though I have not tryed it 
my felf But he that would repeat it, muft take care 
the Liquors be of very good and full Colours. 

S !• Now 



ho] 

Now whilft Bodies become coloured by rciletfting or 
tranfmitting this or that fort of rays more copioufly than 
the reft, it is to be conceived that they ftop and ftifle in 
themfelves the rays which they do not reflector tranfmit. 
For if Gold be foliated and held between your Eye and 
the Light, the Light looks blue, and therefore maffy Gold 
lets into its Body the blue-making rays to be relied ed 
to and fro within it till they be ftopt and ftifled, whilft 
it rellefts the yellow-making outvv^ards, and thereby 
looks yellow. And miuch after the fame manner that 
Leaf-gold is yellow by refledted, and blue by tranfmit- 
ted Light, and maffy Gold is yellow in allpoiitions of 
the Eye ; there are Ibme Liquors as the tinfture of 
luignum Nefhriticum^ and fom.e forts ofGlafs which 
tranfmit one fort of Light moft copioufty^ and refiedt 
another fort, and thereby look of feveral Colours, ac- 
cording to the pofition of the Eye to the Light. But if - 
thefe Liquors or Glaffes were fo thick and mafly that 
no Light could get through them, I queftion not but 
that they would like all other opake Bodies appear of 
one and, the fame Colour in all poiitions of the Eye,, 
though this I cannot yet affirm by experience. For all 
coloured Bodies, fo far as my Qbiervation reaches, may 
be feen through if made fufficiently thin, and therefore 
are in fome m.eafure tranfparent, and differ only in de- 
grees of tranfparency from tinged tranfparent Liquors; 
thefe Liquors, as well as thofe Bodies, by a fufiicient 
thicknefs becoming opake. A tranfparent Body which 
Iboks of any Colour by tranfmitred Light, may alfo.. 
look of the fame Colour by refle&ed Light, the Light 
of that Colour being refteiied by the further furface of 
the Body, or by the Air beyond it. And then the re- 
flected Colour will be dimiiiifhed^ and perhaps ceafe, by 

making 



[ H^- ] 

making the Body very thick, and pitching it on the 
back-fide to diminifh the reflexion of its further furface, 
lb that the Light refleded from the tinging particles 
may predominate. In fuch cafes, the Colour of the re- 
flefted Light will be apt to vary from that of the Light 
tranfmitted. But v^hence it is that tinged Bodies and 
Liquors refleft fome fort of rays, and intromit or tranf- 
mit other forts, Ihall belaid in the next Book. In this 
Propofition I content my felf to have put it paft difpute,^ 
that Bodies have fuch Properties, and thence appear 
coloured. 

PROP. XL PROB. VL 

5y mixing coloured Lights to comfound a Beam of Liohp 
of thejame Colour and NaXvjre 'with a Beam of the Suns'^ 
dtreiH L'^ght^ and therein to experience the truth of the. 
foregoing Trofofitions, 

Let A B C a b c reprefent a Prifm by which the Sun's Fig^ r& 
Light let into a dark Chamber through the Hole F, may. 
be refracted towards the Lens M N, and paint upon it 
at p, q, r, s and t, the uliial Colours violet, blue, green^, 
yellow and red, and let the diverging rays by the re- 
fraftion of this Lens converge again towards X, and. 
there,by the mixture of all thofe their Colours,compound. 
a white according to what was (liewn above. Then let 
another Prifm DEGdeg, parallel to the former, be 
placed at X, to refrad: that white Light upwards to- 
v/ards Y. Let the refrading Angles of the Prifms^,, 
aad their diftances from the Lens be equal, fo that the. 
rays which converged from the Lens towards X, and. 
without refradion, would there have croffed and diver- 
ged again, may by the refradion of the fecond Priim be 

redaced. 



reduced into Parallelifm and diverge no more. For 
then thofe rays will recompofe a Beam of white Light 
XY. If the refracting Angle of either Prifm be the 
bigger, that Prifm mult be fb much the nearer to the 
Lens. You will know when the Prifms and the Lens 
are well fet together by obferving if the Beam of Light 
XY which comes out of the fecond Prifm be perfedly 
white to the very edges of the Light, and at all diftan- 
•ces from the Prifm continue perfedly and totally white 
like a Beam of the Sun's Light. For till this happens, 
the pofition of the Prifms and Lens to one another mult 
be correded, and then if by the help of a long Beam of 
Wood, as is reprefented in the Figure, or by a Tube, 
or fome other fuch inftrument made for that purpofe, 
they be made faft in that fituation, you may try all the 
lame Experiments in this compounded Beam of Light^ 
XY, which in the foregoing Experiments have been 
nrade in the Sun's direft Light. For this compounded 
Beam of Light has the fame appearance, and is endowed 
with all the fame Properties with a direCt Beam of the 
Sun's Light, fo far as my Obfervation reaches. And in 
trying Experiments in this Beam you may by flopping 
any of the Colours p, q, r, s and t, at the Lens, fee how 
the Colours produced in the Experiments are no other 
than thofe which the rays had at the Lens before they 
entered the compolition of this Beam : And by confe- 
quence tiiat they arife not from any new modifications 
of the Light by refraftions and reliexions, but from the 
various feparations and mixtures of the rays originally 
endowed with their colour-making qualities. 

So, for inftance, having with a Lens 4; Inches broad, 
and two Prifms on either Hand 6\ Feet diftant from the 
Lens, made fuch a Beam of compounded Light : to 

examin 



CH3] 

€xamm the reafon of the Colours made by Priiliis^ 1 
refraded this compounded Beam of Light X Y with 
another Prifm HIK kh, and thereby call the ufual prit 
matick Colours P QR S T upon the Paper LV placed be- 
hind. And then by ftopping any of the Colours p, q^ 
r, s, t^ at the Lens^ I found that the fame Colour would 
vanifh at the Paper. So if the purple P was flopped at 
the Lens, the purple P upon the Paper would vanifh, 
and the reft of the Colours would remain unaltered, 
unlefs perhaps the blue, fo far as fome purple latent in 
it at the Lens might be feparated from it by the fol- 
lowing refra£tions. And fo by intercepting the green 
upon the Lens, the green R upon the Paper would va- 
nilh, and fo of the reft ; which plainly Ihev/s, that as 
the white Beam of Light X Y was compounded of fe- 
ve Lights varioufly coloured at the Lens, fo the Co- 
lours w^hich afterwards emerge out of it by new refra- 
ftions are no other than thofe of which its whitenefs 
was compounded. The refradlion of the Prifm HIK 
kh generates the Colours PQR ST upon the Paper, 
not by changing the colorific qualities of the rays, but 
by feparating the rays which had the very fame colorific 
qualities before they entered the compofition of the re- 
fraded Beam white of Light X Y. For otherwife the rays 
which were of one Colour at the Lens might be of ano- 
ther upon the Paper, contrary to w^hat we find. 

So again, to examin the reafon of the Colours of na- 
tural Bodies, I placed fuch Bodies in the Beam of Light 
X Y, and found that they all appeared there of thofe 
their own Colours which they have in Day-light, and 
that thofe Colours depend upon the rays which had the 
fame Colours at the Lens before they enti^ed the compo- 



[H4-] 

fition of that Beam. Thus, for infcancc^Cinnaber illumi- 
nated by this Beam appears of the fame red Colour as in 
Day-light ; and if at the Lens you intercept the green- 
making and blue-making rays^ its rednefs will become 
more full and lively : But if you there intercept the red- 
making rays, it will not any longer appear red, but be- 
come yellow or green, or of fom.e other Colour, accor- 
ding to the forts of rays which you do not intercept. 
So Gold in this Light XY appears of the fame yellow 
Colour as in Day-light, but by intercepting at the Lens a 
due quantity of the yellow-making rays it will appear 
white like Silver (as 1 have tryed) which fiiews that its 
yellownefs arifes from the excefs of the intercepted rays 
tinging that whitenefs with their Colour when they are 
let pals. So the infufion oi Lignum Nefhritlcum ( as I 
have alfo tryed ) when held in this Beam of Light XY, 
looks blue by the reflefted part of the Light, and yellow^ 
by the tranimitted part of it, as when 'tis viewed in Day- 
light, but if you intercept the blue at the Lens the infu- 
fion will lofe its reflefted blue Colour, whilft its tranf- 
mitted red remains perfeft and by the iofs of fome blue- 
making rays vv^herewith it was allayed becomes morein- 
tenie and full. And, on the contrary, if the red and orange- 
making rays be intercepted at Lens, the infuiion will 
iole its tranimitted red, whilfl its blue will remain and 
become more full and perfedl. Which ihews, that the in- 
fufion does not tinge the rays with blue and yellow, but 
- only tranlmit thofe moft copioufly which were red-ma- 
king before, and refleds thofe molt copioufly w^hich were 
blue-making before. And after the fame manner may the 
reafons..of other Phaenomena be examined, by trying 
themx in this artificial Beam of Light X Y. 

THE 



Book I. Part H. Plate I. 




J^i 2a- 



6 ^ ^ ^ F 



Fl^^l,. B,/^ 



i G....-- ^ 



L 5 I 

^7 4 



&_^ 




<Zl -■■■:.. M- 



3 ^ 



IS, ± 

3 \S 2 



^^5- 




Book I. Part n. Plate E. 




sa: 



X Bookl.PartH. Plate m. 




Book 1. Part I.Place R". 




CO 

THE 

SECOND BOOK 



O F 



O P T I C K S. 



PARTI. 



Oifervations concerning the Reflexions^ RefraBions^ and 
Colours of thin tranjfarent Bodies, 

IT has been obferved by others that tranfparent 
Subftances, as Glafs, Water, Air, Jf^r. when made 
very thin by being blown into Bubbles, or otherwife 
formed into Plates, do exhibit various Colours accor- 
ding to their various thinnefs, although at a greater 
thicknefs they appear very clear and colourlefs. In 
the former Book I forbore to treat of thefe Colours^ 
becaufe they feemed of a more difficult confideration, 
and were not neceffary for eftablifhing the Properties 
of Light there difcourfed of. But becaufe they may 
conduce to further difcoveries for completing the 
Theory of Light, efpecially as to the conftitution of 
the parts of natural Bodies, on which their Colours or 
Tranfparency depend ; I have here fet down an ac- 
count of them. To render this Difcourfe fliort and 
diftinCt, I have firft defcribed the principal of my 



[2] 

Obfervations, and then confidered and made ufe of 
them. The Obfervations are thefe. 

O B S. I. 

Compreffing two Prifms hard together that their 
Sides (which by chance were a very little convex)might 
fomewhere touch one another : I found the place in 
which they touched to become abfolutely tranfparent^ 
as if they had there been one continued piece of Glafs. 
For when the Light fell fo obliquely on the Air, which 
in other places was between them^as to be all refleded ; 
it feemed in that place of contad to be wholly tranf- 
mitted, infomuch that v/hen looked upon, it appeared 
like a black or dark Spot, by reafon that little or no 
fenfible Light was refleded from thence, as from other 
places; and when looked through it feemed (as it were) 
a hole in that Air w^iich was formed into a thin Plate^ 
by being compreffed between the Glaffes. And through 
this hole Objects that were beyond might be feen di- 
ftindly, which could not at all be feen through other 
parts of the Glaffes where the Air was interjacent. Al- 
though the Glaffes were a little convex, yet this tranf- 
parent Spot was of a confiderable breadth,which breadth 
feemed principally to proceed from the yielding inwards 
of the parts of the Glaffes, by reafon of their mutual 
preffure. For by preffing them very hard together it 
would become much broader than otherwile. 



OBS. 



3] 

O B S. 11. 

When the Plate of Air, by turning thePrifms about 
their common Axis., became fo little inclined to the in- 
cident RaySj that fome of them began to be tranfmit- 
ted, there arofe in it many flender Arcs of Colours 
which at fir ft were fhaped almoft like the Conchoid, 
as you fee them delineated in the firft Figure. AndF^^^ ^ 
by continuing the motion of the Prifms, thefe Arcs in- 
creafed and bended more and more about the faid tranf- 
--parent Spot, till they were completed into Circles or 
Rings incompaffing it, and afterwards continually grew 
more and m.ore contrafted. 

Thefe Arcs at their firft appearance were of a violet 
and blue Colour, and between them were white Arcs 
of Circles, which prefently by continuing the motion of 
the Prifms became a little tinged in their inward Limbs 
with red and yellow, and to their outward Limbs the 
blue was adjacent. So that the order of thefe Colours 
from the central dark Spot, was at that time white, 
blue, violet ; black ; red, orange, yellow, white, blue, 
violet, Js'r. But the yellow and red were much fainter 
than the blue and violet. 

The motion of the Prifms about their Axis being con- 
tinued, thefe Colours contracted more and more,ftirink= 
ing towards the whitenefs on either fide of it, until they 
totally vanifhed into it. And then the Circles in thofe 
•parts appeared black and white, without any other Co- 
lours intermixed. But by further moving the Prifms 
about, the Colours again emerged out of the whitenefs, 
the violet and blue as its inward Limb, and at its out- 

A a 2- 



[4] 

ward Limb the red and yellow. So that now their order 
from the central Spot was white, yellow, red ; black ; 
violet, blue, white, yellow, red, Oc, contrary to what 
it was before. 

O B S. Ill 

When the Rings or fome parts of them appeared only 
black and white, they were very diftin£t and v/ell de- 
fined, and the backnefs feemed as intenfe as that of 
the central Spot. Alfo in the borders of the Rings,, 
where the Colours began to emerge out of the white- 
nefs, they were pretty diftinCt, which made them vi- 
iible to a very great Multitude. I have fom.etimes 
numbred above thirty Succeffions ( reckoning every 
black and white Ring for one Succeffion ) and feen 
more of them., which by reafon of their fmalnefs I could 
not number. But in other Pofitions of the Prifms, at 
which the Rings appeared of many Colours, I could not 
diftinguifh above eight or nine of them, and the exte- 
rior of thofe were very confufed and dilute. 

In thefe two Obfervations to fee the Rings diftinft,^ 
and without any other Colour than black and white,! 
found it neceflary to hold my Eye at a good diftance 
from them. For by approaching nearer, although in the 
fame inclination of my Eye to the plane of the Rings, 
there emerged a blueifh Colour out of the white, 
which by dilating it felf more and more into the black 
tendred the Circles lefs diftind, and left the white a 
little tinged with red and yellow. I found alfo by 
looking through a flit or oblong hole , which was 
flarrower than, the Pupil of my Eye, and held clofe to 

it 



[5] 

it parallel to the Prlfms^ I could fee the Circles much 
diftinder and vifible to a far greater number than 
otherwife. 

O B S. IV. 

To obferve more nicely by the order of the Colours- 
which arofe out of the white Circles as the Rays be- 
came lefs and lefs inclined to the plate of Air; 1 took 
two Object Glaffes, the one a Plano-convex for a four- 
teen-foot Telefcope, and the other a large double con- 
vex for one of about fifty-foot; and upon this^laying the 
other with its its plane-fide downwards, I prefled them 
llowly together^to make the Colours fucceffively emerge 
in the middle of the Circles, and then flowly lifted 
the upper Glafs from the lower to make them fuccef- 
fively vanilh again in the fame place. The Colour, 
which by preffing the Glaffes together emerged laft in 
the middle of the other Colours, would upon its firft 
appearance look like a Circle of a Colour ahnoft uni- 
form from the circumference to the center , and by 
comprefling the Glaffes ftill more, grow continually 
broader until a new Colour emerged in its center, and 
thereby it became a Ring encompafling that new Co^ 
lour. And by comprefling the Glaffes ftill more, the 
Diameter of this Ring would encreafe, and the breadth 
of its Orbit or Perimeter decreafe until another new 
Colour emerged in the center of the laft : And fo on 
until a third, a fourth, a fifth, and other following 
new Colours fucceflively emerged there, and became 
Rings encompaffmg the innermoft Colour, the laft of 
which was the black Spot. And, on the contrary, by 



[6 

lifting up the upper Glafs from the lower, the diameter 
of the Rings would decreafe, and the breadth of their 
Orbit encreafe, until their Colours reached fucceffively 
to the center ; and then they being of a confiderable 
breadth, I could more eafily difcern and diltinguifh 
their Species than before. And by this means 1 ob- 
ferved their Succeffion and Quantity to be as fol- 
loweth. 

Next, to the pellucid central Spot made by the con- 
taft of the Glaffes fucceeded blue, white, yellow, and 
red, the blue was fo little in quantity that I could not 
difcern it in the circles made by the Prifms, nor could 
I well diftinguifh any violet in it, but the yellow and 
red were pretty copious, and feemed about as much 
in extent as the white , and four or five times more 
than the blue. The next Circuit in order of Colours 
immediately encompaffing thefe were violet, blue, 
green, yellow, and red, and thefe were all of them co- 
pious and vivid, excepting the green, which was very 
little in quantity, and feemed much more faint and 
dilute than the other Colours. Of the other four, the 
violet was the leaft in extent , and the blue lefs than 
the yellow or red. The third Circuit or Order was 
purple, blue, green, yellow, and red ; in which the 
purple feemed more reddifli than the violet in the 
former Circuit, and the green was much more confpi- 
cuous, being as brifque and copious as any of the other 
Colours, except the yellow ; but the red began to be 
a little faded, inclining very much to purple. After 
this fucceeded tlie fourth Circuit of green and red. The 
green was very copious and lively, inclining on the one 
lide to blue, and on the other fide to yellow. But in 

this 



C7], 

this fourth Circuit there was neither violet, blue, nor 
yellow, and the red was very imperfed and dirty. 
Alfo the fucceeding Colours became more and more im- 
perfed and dilute, till after three or four Revolutions 
they ended in perfect whitenefs. Their Form, when the 
Glaffes were moft compreffed fo as to make the black 
Spot appear in the Center, is delineated in the Second 
Figure ; where a^ b^ r, J, e ;/, o, /?, i, ^ : /, m^ n^ o^ f : q^ ?- ; F^g'. ^ 
J", t : v^x'.y denote the Colours reck'ned in order from 
the center, black, blue, white, yellow, red : violet, 
blue, green, yellow, red : purple, blue, green, yellow, 
red : green, red : greenifh blue, red : greenilTi blue^ 
pale red : greenifli blue, reddiih white, 

O B S. V. 

To determine the interval of the Glaffes, or thick- 
nefs of the interjacent Air, by which each Colour was 
produced, I meafured the Diameters of the firft fix 
Rings at the moft lucid part of their Orbits, and fqua- 
ring them, I found their Squares to be in the Arith- 
metical Progreffion of the odd Numbers, 1,3.5.7,9.11. 
And fince one of thefe Glaffes was Plain, and the other 
Spherical, their Intervals at thofe Rings muft be in the 
fame Progreffion. I meafured alfo the Diameters of 
the dark or faint Rings between the more lucid Co- 
lours, and found their Squares to be in the Arithme- 
tical Progreffion of the even Numbers, 1. 4.. 6c 8. 10= i cj. 
And it being very nice and difficult to take thefe mea- 
fures exaftly ; I repeated them at divers times at divers 
parts of the Glaffes, that by their Agreement I might 
be confirmed in them.. And the fame Method I ufed in 



determining fome others of the following Obferva* 
tions. 

O B S. VI. 

The Diameter of the fixth Ring at the moft lucid 
part of its Orbit was ^^ parts of an Inch, and the Dia- 
meter of the Sphere on which the double convex Ob- 
jeft'Glafs was ground was about loa Feet, and hence 
I gathered the thicknefs of the Air or Aereal Interval 
of the Glafles at that Ring. But fome time after, fuf- 
ped:ing that in making this Obfervation I had not de- 
termined the Diameter of the Sphere with fufficient ac- 
curatenefs, and being uncertain whether the Plano- 
convex Glafs was truly plain, and not fomething con- 
cave or convex on that fide which I accounted plain ; 
and whether I had not preffed the Glafles together, as 

I often did, to make them touch, (for by prefling fuch 
Glafles together their parts eafily yield inwards, and 
the Rings thereby become fenfibly broader than they 
would be, did the Glafles keep their Figures.) I re- 
peated the Experiment, and tound the Diameter of 
the fixth lucid Ring about 7^ parts of an Inch. I re- 
peated the Experiment alfo with fuch an Objedt-Glafs 
of another Telefcope as I had at hand. This was a double 
convex ground on both fides to one and the fame 
Sphere, and its Focus was diftant from it 8^j Inches. 
And thence, if the Sines of incidence and refra£tion of 
the bright yellow Light be aflumed in proportion as 

II to 17, the Diameter of the Sphere to which the 
Glafs was figured will by computation be found 1 82 In- 
ches. This Glafs I laid upon a flat one, fo that the 

black 



black Spot appeared in the middle of the Rings of Colours 
without any other preffure than that of the weight of 
the Glafs. And now meafuring the Diameter of the 
fifth dark Circle as accurately as 1 could, I found it the 
fifth part of an Inch precifely. This meafure was taken 
with the points of a pair of Compafles on the upper fur- 
face on the upper Glafs, and my Eye was about eight 
or nine Inches diftance from the Glafs, almoft perpen- 
dicularly aver it, and the Glafs w^as I of an Inch thick, 
and thence it is eafy to colleft that the true Diameter 
of the Ring between the Glaflfes was greater than its 
mcafured Diameter above the Glaflfes in the proportion 
of 80 to 79 or thereabouts, and by confequence equal 
to ~ paTts of an Inch, and its true Semi-diameter equal 
to ^ parts. Now as the Diameter of the Sphere ( 1 81 In- 
ches) is to the Semi-diameter of this fifth dark Ring 
( ~ parts of an Inch ) fo is this Semi-diameter to the 
.thicknefs of the Air at this fifth dark Ring ; which is 
therefore ^, or j^^ parts of an Inch, and the fifth 
part thereof; viz. the sgy^^th part of an Inch, is the 
thicknefs of the Air at the firft of thefe dark Rings. 

The fame Experiment I repeated with another dou- 
ble convex Objeft-glafs ground on both fides to one and 
the fame Sphere. Its Focus was diftant from it i68[ 
Inches, and therefore the Diameter of that Sphere was 
184 Inches. This Glafs being laid upon the fame 
plain Glafs, the Diameter of the fifth of the dark 
Rings, when the black Spot in their center appeared 
plainly without preffing the Glaflfes , was by the mea» 
fure of the Compaflfes upon the upper Glafs --^ parts 
of an Inch, and by confequence between the Glafles it 
waS|^. For the upper Glafs was ^ of an Inch thick^ 

Bb and 



[lo] 

and my Eye was diftant from it 8 Inches. And a third 
proportional to half this from the Diameter of the 
Sphere is gglfo parts of an Inch. This is therefore the 
thicknefs of the Air at this Ring^ and a fifth part there- 
of^ vit. the ggg^o^h part of an Inch is the thicknefs there- 
of at the firft of the Rings as above. 

I tryed the fame thing by laying thefe Objedt-Glaffes 
upon liar pieces of a broken Looking-gkifs, and found 
the fame meafures of the Rings : Which makes me 
rely upon them till they can be determined more ac- 
curately by GlalTes ground to larger Spheres^ though 
in fuch Glaffes greater care muft be taken of a true 
plain. 

Thefe Dimenfions were taken when my Eye was 
placed almoft perpendicularly over tlie Glaffes^ being 
about an Inch ^ or an Inch and a quarter^ diftant from 
the incident rays^ and eight Inches diftant from the 
Glafs ; fo that the rays were inclined to the Glafs in an 
Angle of about 4. degrees. Whence by the following 
Obfervation you will underftand ^ that had the rays 
been perpendicular to the Glaffes., the thicknefs of the 
Air at thefe Rings would have been lefs in the propor- 
tion of the Radius to the fecant of 4 degrees, that is of 
loooo. Let the thickneffes found be therefore dimi- 
nillied in this proportion, and they will becomie — ^ and 
&9^5 or ( to ufe the neareft round number ) the g^th 
part of an Inch. This is the thicknefs of the Air at the 
darkeft part of the firft dark Ring made by perpendi- 
cular rays, and half this thicknefs multiplied by the 
progreffion,i,3,5,7,9, i \^c. gives the thickneffes of the 
Air at the moft luminous parts of all the brighteft 
Rings, viz. :^^r.T^,,,,T^^,Tjt;,,^c, their arithmetical 

means 



[II] 

, b'/T. being its thickneffes at the 



iliedllb i^acoo? 17600CJ i7«oo . _ 

darkeft parts of all the dark ones 

O B S. VII. 

The Rings were leaf!: when my Eye was placed per- 
pendicularly over the Glaffes in the Axis of the Rings : 
And when I viewed them obliquely they became big- 
ger, continually fwelling as I removed my Eye further 
from the Axis. And partly by meafuring the Diameter 
of the fam.e Circle at feveral obliquities of my Eye, 
partly by other means, as alfo by making ufe of the 
two Frifms for very great obliquities. I found its Dia- 
meter, and confequently the thicknefs of the Air at its 
perimeter in all thofe obliquities to be very nearly in the 
proportions exprefled in this Table. 



Angle 


of In- 


Angle of Re- 


Diameter of 


Thicknefs of 


cidence 


on the 


fra^ion into 


the King, 


the Air. 


Air, 




the Air, 






deg. 


min. 








00 


00 


00 00 


10 


10 


06 


16 


10 00 


lorj 


1°^ . 


11 


45 


10 00 


1°^ 


lOf 


18 


49 


50 00 


I of 


II-: 


H 


30 


40 00 


"-: 


n 


29 


5Z 


50 00 


i2i 


15^ 


59 


58 


60 00 


14 


10 


35 


47 


65 00 


157 


^3^ 


37 


19 


70 00 


i6| 


i8f 


.38 


33 


75 00 


195 


37, 


39 


^7 


80 00 


aaf 


52J 


40 


00 


85 00 


29 


Hi 


40 


1 1 


90 00 


35 


iaa| 








i5b 2 





in 



[12] 

In the two firft Columns are expreffed the QbHq;Uities 
of the incident and emergent rays to the plate of the 
Air, that is^ their angles of incidence and refradion. In 
the third Column the Diameter of any coloured Ring 
at thofe obliquities is expreffed in parts, of which ten 
conftitute that Diameter when the rays are perpendicu- 
lar. And in the fourth Column the thickneis of the Air 
at the circumference of that Ring is expreffed in parts 
of which alio ten conftitute that thicknefs when the rays« 
are perpendicular. 

And from thefe meafures I feem to gather this Rule r 
That the thicknefs of the Air is proportional to the fe-* 
cant of an angle, whofe Sine is a certain mean propor- 
tional between the Sines of incidence and retraftion.,- 
And that mean proportional, fo far as by thefe meafures^ 
I can determine it, is the firft of an hundred and fix. 
arithmietical mean proportionals between thofe Sines 
counted from the Sine of refraction when the refra- 
filion is made out of the Glafs into the plate of Air, or 
from the Sine of incidence when the refraction is 
made out of the plate of Air into the Glafs o 

O B S. VIIL 

The dark Spot in the middle of the Rings increafed 
alfo by the obliquation of the Eye, although almoft in- 
fenfibly. But if infteadoftheObjeft-Glaffes tbePrifms 
were made ufe of, its increafe was more manifeft when 
viewed fo obliquely that no Colours appeared about it. 
It was leaft when the rays were incident moft obliquely 
on the interjacent Air, and as the obliquity decreafed 
it increafed more and more imtil the coloured Rings ap- 
peared. 



C 13 ]. 

peared^ and then d£creafed agaiia^ but rtot fo much as 
it increafed before. And hence it is evident, that tlie 
tranfparency was not only at the abiblute contaft of the 
Glafles, but alfo where they, had fome Httle interval. 
1 have ibmetimes obferved the Diameter of that Spot to 
be between half and two fifth parts of the Di-ameter of 
the exterior circumference of the red in the firft cir- 
cuit or revolution of Colours when viewed almoft per- 
pendicularly ; whereas when viewed obliquely it hath 
wholly vanilhed and become opake a*nd white like the 
other parts of the Glafs ; whence it may be colledted 
that the GlalTes did then fcarcely, or not at all, touch 
one another, and that their interval at the perimeter 
of that Spot when viewed perpendicularly was about a 
fifth or fixth part of their interval at the circumference 
of the faid red. 

O B S. IX. 

By looking through the two contiguous Objeff- 
Glaffes, I found that the interjacent Air exhibited Rings 
of Colours, as well by tranfmitting Light as by reflect- 
ing it. The central Spot was now white, and from it 
the order of the Colours were yellowifh red ; black ; 
violet, blue, white, yellow, red; violet, blue, green^ 
yellow, red, '^c\ But thefe Colours were very faint 
and dilute unlefs when the Light was trajefted very 
obliquely through the Glafles : For by that means they 
became pretty vivid. Only the firft yellowifh red, like 
the blue in the fourth Qbfervation, was fo little and 
faint as fcarcely to be difcerned. Comparing the co- 
loured Riiigs made by reflexion, with thefe made by 

tranl" 



tranfmiffion of the Light ; I found that white was op- 
pofite to black, red to blue, yellow to violet, and green 
to a compound of red and violet. That is, thofe parts 
oftheGlafs were black when looked through, which 
when looked upon appeared white, and on the con- 
trary. And fo thofe which in one cafe exhibited blue, 
did in the other cafe exhibit red. And the like of the 
K^". 3- other Colours. The manner you have reprefen ted in 
the third Figure, where A B, C D, are the furfaces of 
the Glafles contiguous at E, and the black lines be- 
tween them are their diftances in arithmetical progref- 
fion, and the Colours written above are feen by re- 
flected Light, and thofe below by Light tranfmitted. 

O B S. X. 

Wetting the Objed-Glafles a little at their edges, 
the water crept in flowly between them, and the Cir- 
cles thereby bec-ame lefs and the Colours more faint : 
Infomuch that as the water crept along one half of 
them at w^hicli it firft arrived would appear broken oif 
from the other half, and contracted into a lefs room. 
By meafuring them I found the proportions of their 
Diameters to the Diameters of the like Circles made by 
Air to be about feven to eight, and confequently the in- 
tervals of the Glafles at like Circles, caufed by thofe 
two mediums Water and Air,are as about three to four. 
Perhaps it may be a general Rule, That if any other 
medium more or lefs denfe than water be comprefled 
between the Glafles, their intervals at the Rings caufed 
thereby will be to their intervals caufed by interjacent 

/Vir* 



J ^5 1 

Air, as the Sines are which meafure the refradtion made 
out of that medium into Air. 

OB S. XL 

When the water was between the Glafles, if I pref- 
fed the upper Glafs varioufly at its edges to make the 
Rings move nimbly from one place to another, a little 
white Spot would immediately follow the center of 
them, which upon creeping in of the ambient water 
into that place w^ould prefently vanifh. Its appearance 
was fuch as interjacent Air would have caufed, and it- 
exhibited the fame Colours. But it was not Air, for 
where any bubbles of Air were in the water they would 
not vanifh.. The reflexion muft have rather been caufed 
by^a^ fuEtiler medium, which could recede through the,, 
GlalTes at the creeping in of the water, 

OB S. XII. 

Thefe Obfervations were made in the open Air. Bute 
further to examin the efFeds of coloured Light falling 
on the Glafles, I darkened the Room, and viewed them 
by reflexion of the Colours of a Prifm caft on a Sheet 
of white Paper, my Eye being fo placed that I could 
fee the coloured Paper by reflexion in the Glafles, as. 
in a Looking-glafs. And by this means the Rings be- 
came diftin£ter and vifible to a far greater number than- 
in the open Air. I have fometimes feen more than 
twenty of them, whereas in the open Air I could not 
difcern above eight or nine. 



Q 



Id] 

O B S. XII I. 

Appointing an affiftant to move the Prifm to and 
fro about its Axis, that all the Colours might fuccef- 
fively fall on that part of the Paper which I faw by 
reflexion from that part of the Glaffes, v/here the Cir- 
cles appeared, fo that all the Colours might be fuccef- 
lively refledled from the Circles to my Eye whilfl: I held 
it immovable, I found the Circles which the red Light 
made to be manifeftly bigger than thofe which were 
made by tlie blue and violet. And it was very plea- 
fant to fee them gradually fwell or contrad: according 
as the Colour of the Light was changed. The inter- 
val of the Glafles at any of the Rings when they were 
made by the utmoft red Light, was to their interval at 
the fame Ring when made bythe utmoft violet, greater 
than as 3 to a,and lefs than as 1 9 to 8,by the moft of my 
Obfervations it was as 14. to 9. And this proportion 
feemed very nearly the fame in all obliquities of my 
Eye ; unlets when two Prifms were made ufe of inftead 
of the Objeft-Gtaffes. For then at a certain great 
obliquity of my Eye, the Rings made by the fet^ral 
Colours feemed equal, and at a greater obliquity thofe' 
made by the violet would be greater than the fame 
Rings made by the red. The refraftion of the Prifm 
in this cafe caufing the moft refrangible rays to fall 
more obliquely on that plate of the Air than the leaft 
refrangible ones. Thus the Experiment fucceeded in 
the^ coloured Light, which was fufficiently ftrong and 
copious to make the Rings fenfible. And thence it 
may be gathered, that if the moft refrangible and leaft 

refran- 



[I?] 

refrangible rays had been copious enough to make the 
Rings feniible without the mixture of other rays, the 
proportion which here was 14 to 9 would have been a 
little greater^ fuppofe 14. » or 14. Uo 9. 

O B S. XIV. 

Whilil the Prifm was turn'd about its Axis with an 
uniform motion, to make all the feveral Colours fall 
fucceffively upon the Objeft-Glafles, and thereby to 
make the Rings contraft and dilate : The contraftion 
or dilation of each Ring thus made by the variation of 
its Colour was fwiftcft in the red, and floweft in the 
violet, and in the intermediate Colours it had inter- 
mediate degrees of celerity. Comparing the quantity 
o{ contraftion and dilation made by all the degrees of 
each Colour, I found that it was greateft in the red ; 
lefs in the yellow, ftill lefs in the blue, and leaft in the 
violet. And to make as juft an eftimation as I could of the 
proportions of their contractions or dilations, I obferved 
that the w^hole contraftion or dilation of the Diameter 
of any Ring made by all the degrees of red, was to that 
of the Diameter of the fame Ring made by all the de- 
grees of violet, as about four to three, or five to four, and 
that when the Light was of the middle Colour between 
yellow and green, the Diameter of the Ring was very 
nearly an arithmetical mean between the greateft Dia- 
meter of the fame Ring made by die outmoft red, and 
the leaft Diameter thereof made by the outmoft violet : 
Contrary to what happens in the Colours of the oblong 
Spedrum made by the refradion of a Prifm, where the 
red ismoft contracted, the violet moft expanded, and 

D d * in 



[i8] 

ill the midft of all the Colours is the confine of green 
and blue. And hence 1 feem to colleft that the thick- 
neffes of the Air between the Glaffes there, where the 
Ring is fucceffively made by the limits of the five prin- 
cipal Colours (red, yellow, green, blue, violet) in order 
( that is, by the extreme red, by the limit of red and 
yellow in the middle of the orange, by the limit of 
yellow^ and green, by the limit of green and blue, by 
the limit of blue and violet in the middle of the in- 
digo, and by the extreme violet ) are to one another 
very nearly as the fix lengths of a Chord which found 
the notes in a fixth Major, fol^ la^ ml^ fa^ fol^ la. But 
it agrees fomething better with the Obfervation to fay, 
that the thicknefles of the Air between the Glaffes there, 
where the Rings are fucceffively made by the limits of 
the feven Colours, red, orange, yellow, green, blue, in- 
digo, violet in order, are to one another as the Cube- 
roots of the Squares of the eight lengths of a Chord^ 
which found the notes in an eighth , fol^ la^ fa^ fol^ la^ 
mij fii^ fol ; that is, as the Cube-roots of the Sq[uares 
of the Numbers, i,|;a, i i, f, tI,i-- 

OB a XV. 

Thefe Rings were not of various Colours like thofe 
made in the open Air^ but appeared all over of that 
prifmatique Colour only with which they were illu- 
minated. And by projefting the prifmatique Colours 
immediately upon the Glaffes, 1 found that the Light 
which fell on the dark Spaces which were between 
the coloured Rings , was tranfmitted through the 
Glaffes without any variation of Colour. For on a 

white 



J9] 

white Paper placed behind, it would paint Rings of 
the fame Colour with thofe which were reflefted, and 
of the bignefs of their immediate Spaces. And from 
thence the origin of thefe Rings is manifeft ; namely, 
That the Air between the GlajQTes, according to its va- 
rious thicknefs, is difpofed in fome places to reflied:, 
and in others to tranfmit the Light of any one Co- 
lour (as you may fee reprefented in the fourth Figure ) pig 
and in the fame place to refled that of one Colour 
where it tranfmits that of another. 



O B S. XVL^ 

The Squares of the Diameters of thefe Rings made 
any prifmatique Colour were in arithmetical pro- 
greffion as in the fifth Obfervation. And the Diameter 
of the fixth Circle, when made by the citrine yellow^ 
and viewed almoit perpendicularly, was about f|;7 parts 
of an Inch, or a little lefs, agreeable to the iixth Ob- 
fervation. 

. The precedent Obfervations were made with a rarer 
thin medium, terminated by a denfer, fuchas was Air 
or Water compreffed between two Glaffes. In thofe 
that follow are fet down the appearances of a denfer 
medium thin^'d within a rarer, fuch as are plates of 
Mufcovy-glafs, Bubbles of Water, and fome other thin 
fubftances terminated on all fides with Air» 



U uJii^ 



d 2 OfiS. 



O B S. XVII. 

If a Bubble be blown with Water firft made tenacious 
by diflblving a little Soap in it, 'tis a common Obfer- 
varion, that after a while it will appear tinged with a 
great variety of Colours. To defend theie Bubbles 
from being agitated by the external Air (w- hereby their 
Colours are irregularly moved one among another, fo 
that no accurate Obfervation can be made of them,) as 
foon as 1 had blown any of them I covered it with a 
clear Glafs, and by that means its Colours emerged in 
a very regular order, like fo many concentrick Rings 
incompaffing the top of the Bubble. And as the 
Bubble grew thinner by the continual fubfiding of the 
Water, thefe Rings dilated ilow^ly and over-fpread the 
ivhole Bubble, defcending in order to the bottom of it, 
where they vaniihted fucceffively. In the mean while, 
after all the Colours were emerged at the top, there 
grew in the Center of the Rings a fmall round black 
Spot, like that in the firft Obfervation, which conti- 
nually dilated it felf till it became fometimes more than 
I or I of an Inch in breadth before the Bubble broke. 
At firft I thought there had been no Light reflefted from 
the Water in that place, but obferving it more cu- 
rioufly, I faw within it feveral fmaller round Spots, 
which appeared much blacker and darker than the reft, 
whereby I knew that there was fome reflexion at the 
other places which were not fo dark as thofe Spots. 
And by further tryal I found that I could fee the Images 
of fokiue things ( as of a Candle or the Sun ) very faint- 
ly reflected, not only from the great black Spot, but 

alio 



[21] 

alio from the little darker Spots whicii were with- 
in it. 

Befides the aforefaid coloured Rings there would 
often appear fmall Spots of Colours, afcending and de- 
fcending up and down the fides of the Bubble, by reafon 
of fome inequalities in the fubfiding of the Water. 
And fometimes fmall black Spots generated at the fides 
would afcend up to the larger black Spot at the top of 
the Bubble, and unite with it. 

O B S. XVIIL 

Becaufe the Colours of thefe Bubbles were more ex- 
tended and lively than thofe of the Air thin'd between 
two GlafiTes, and fo more eafy to to diftinguilhed , I 
fhail here give you a further delcriptior^ of their order,, 
as they were obferved in viewing them by reflexion of 
the Skies when of a white Colour, whilft a black Sub- 
Itance was placed behind the Bubble. And they were 
thefe, red, blue; red, blue; red, blue; red, green ;. 
red, yellow, green, blue, purple y red, yellow, green,_ 
blue, violet ; red, yellow, white, blue, black.. 

The three firft Succeffions of red and blue w^ere very 
dilute and dirty, efpecially the firft, where the red 
feemed in a manner to be white. Among thefe there, 
was fcarce any other Colour fenfible befides red and 
blue, only the blues ( and principally the fecond blue ) 
inclined a little to green. 

The fourth red was alfo dilute and dirty, but not 
fo much as the former three ; after that fucceeded little 
or no yellow, but a copious green, which at firft incli- 
ned a little to yellow, and then became a pretty brifque 

and: 



22 

and good willow green, and afterwards changed to a 
bluiih Colour; but there fucceeded neither blue nor 
violet. 

The fifth red at firft inclined very much to purple, 
and afterwards became more bright and brifque, but 
yet not very pure. This- was fucceeded with a very 
bright and intenfe yellow, which w^as but little in 
quantity, and foon changed to green : But that green 
was copious and fomething more pure, deep and lively, 
than the former green. After that followed an excel- 
lent blue of a bright sky-colour, and then a purple, 
which was lefs in quantity than the blue, and much 
inclined to red. 

The fixth Red was at firft of a very fair and lively 
Scarlet, and foon after of a brighter Colour , being 
very pure and brifque , and the beft of all the 
reds. Then after a lively orange followed an intenle 
bright and copious yellow, which was alfo the beft 
of all tl;ie yellows, and this changed firft to a greenifli 
yellow, and then to a greenilh blue ; but the green 
between the yellow and the blue, was very little and 
dilute, feeming rather a greenilh white than a green. 
The blue w^hich fucceeded became very good, and of a 
very fair bright sky-colour, but yet fomething inferior 
to the former blue ; ^and the violet was intenfe and 
deep with little or no rednefs in it. And lefs in quan- 
tity than the blue. 

In the laft red appeared a tinfture of fcarlet next 
to violet, which foon changed to a brighter Colour, 
inclining to an orange ; and the yellow which followed 
was at firft pretty good and lively , but afterwards it 
grew more dilute, until by degrees it ended in perfed 

wliite- 



[23] 

whitenefs. And this whitenefs, if the Water was very 
tenacious and well-tempered, would flowly fpread and 
dilate it felf over the greater part of the Bubble ; con- 
tinually growing paler at the top, w^here at length it 
would crack in many places, and thofe cracks, as they 
dilated, would appear of a pretty good, but yet obfcure 
and dark sky-colour; the white betvs^een the blue Spots 
diminiihing, until it refembled the threds of an irre- 
gular Net- work, and foon after vanifhed and left all 
the upper part of the Bubble of the faid dark blue 
Colour. And this Colour, after the aforeiaid manner, 
dilated it felf downwards , until fometimes it hath 
overfpread the whole Bubble. In the mean while at 
the top, which was of a darker blue than the bottom, 
and appeared alfo full ofm.any round blue Spots, fome- 
thing; darker than the reft . there would emerge one 

D 7 

or more very black Spots, and v/ithin thofe other Spots 
of an intenfer blacknefs, which I mentioned in the 
former Obfervation ; and thefe continually dilated 
themfelves until the Bubble broke» 

If the Water was not very tenacious the black Spots 
would break forth in the white, without any fenlible 
intervention of the blue. And fometimes they would 
break forth within the precedent yellow , or red, or 
perhaps within the blue of the fecond order, before 
the intermediate Colours had time to difplay them- 
felves. 

By this defcriptioB you may perceive how great an 
affinity thefe Colours have with thofe of Air defcri- 
bed in the fourth Obfervation, although fet down in 
a contrary order, by reafon that they begin to appear 
when the Bubble is thickeft , and are moll conve- 
niently 



Ch] 

niently leckoned from the loweft and thickeft part of 
the Bubble upwards. 

O B S. XIX. 

Viewing in feveral oblique pofitions of my Eye 
the Rings of Colours emerging on the top of the Bubble, 
I found that they were fenfibly dilated by increafing 
the obliquity , but yet not fo much by far as thofe 
made by thin'd Air in the feventh Obfervation. For 
there they w^ere dilated fo much as, when viewed 
moft obliquely, to arrive at a part of the plate more 
than twelve times thicker than that where they ap- 
peared when viewed perpendicularly ; whereas in this 
cafe the thicknefs of the Water, at which they arrived 
when viewed moft obliquely, was to that thicknefs 
which exhibited them by perpendicular rays, fome- 
thing lefs than as 8 to 5. By the beft of my Obfervations 
it was between 15 and 15I to 10, an increafe about 
14. times lefs than in the other cafe. 

Sometimes the Bubble would become of an uniform 
thicknefs all over, except at the top of it near the black 
Spot, as I knew, becaufe it would exhibit the fame 
appearance of Colours in all pofitions of the Eye. And 
then the Colours which were feen at its apparent cir- 
cumference by the obliqueft rays, would be different 
from thofe that were feen in other places, by rays lefs 
oblique to it. And divers Spectators might fee the 
fame part of it of differing Colours, by viewing it at 
very differing obliquities. Now obferving how much 
the Colours at the fame places of the Bubble, or at di- 
vers places of equal thicknefs , were varied by the 

feveral 



mi 

fevcral obliquities of the rays ;.. by the affiftance of the 
4th, i+th, 1 6th and 18th Obfervations, as they are 
hereafter explained, I colleft the thicknefs of the Water 
requifite to exhibit any one and the fame Colour, at fe« 
veral obliquities , to be very nearly in the proportion 
exprefled in this Table* 



Ificidence on 
the Water, 



Refraction in- I Thicknefs of 
totheWaterA the Water » 




In the two firft Columns are exprefled the obliqui- 
ties of the rays to the fuperficies of the Water, that 
is, their Angles of incidence and refraction. Where 
I fuppofe that the Sines which meafure them are in 
round numbers as 3 to 4, though probably the diflb- 
lution of Soap in the Water ^ may a little alter its 
refradive Vertue. In the third Column the thicknefs 
of the Bubble, at which any one Colour is exhibited 
in thofe feveral obliquities, is expreft in parts,of which 
ten conftitute that thicknefs when the rays are perpen= 
dicular, x 

I have fometimes obferved, that the Colours which 
arife on polifhed Steel by heating it, or on Bell-metal^ 
and fome other metalline fubftances. when melted and 







2($] 

poured on the ground , where they may cool in the 
open Air, have, like the Colours of Water-bubbles, 
been a little changed by viewing them at divers ob- 
liquities, and particularly that a deep blue^ or violet, 
when viewed very obliquely, hath been changed to a 
deep red. But the changes of thefe Colours are not fo 
great and fenfible as of thofe made by Water. For the 
Scoria or vitrified part of the Metal, which moft Me- 
tals wlien heated or melted do continually protrude, 
and fend out to their furface, and which by covering 
the Metals in form of a thin glaffy skin, caufes thefe 
Colours, is much denfer than Water ; and I find that 
the change made by the obliquation of the Eye is leaft. 
In Colours of the denfeft thin fubftances. 

OB S. XX. 

As in the ninth Obfervation, fo here, the Bubble, by 
Iranfmitted Light, appeared of a contrary Colour to 
that which it exhibited by reflexion. Thus when the 
Bubble being looked on by the Light of the Clouds re- 
fledJed from it, fecmed red at its apparent circumfe- 
rence, if the Clouds at the fame time, or immediately 
after, were viewed through it, the Colour at its cir- 
cumference would be blue. And, on the contrary^ 
when by reflefted Light it appeared blue, it would ap- 
pear red by tranfmitted Light.. 

O B S. XXL 

By wetting very thin plates of Mufcovy-glafs, wbofe 
thinnefs made the like ^ Colours appear, the Colours 

became 



[27] 

became more faint and languid j efpeeiaUy by wetting 
the plates on that fide oppofite to the Eye : But I could 
not perceive any variation of their fpecies. So then 
the thicknefs of a plate requifite to produce any Co^ 
lour, depends only on the denfity of the plate, and 
not on that of the ambient medium: And hence, by the 
loth and i6th Obfervations, may be known the thick- 
nefs which Bubbles of Water, or Plates of Mufcovy« 
glafs, or other fubftances, have at any Colour pro- 
duced by them. 

O B S. XXIL 

A thin tranfparent Body, which is denfer than its 
ambient medium, exhibits more brifque and vivid Co^ 
lours than that which is fo much rarer; as I have 
particularly obferved in the Air and Glafs, For blow- 
ing Glafs very thin at a Lamp-furnace, thofe plates \f^'^^'fr^ 
incompaffed with Air did exhibit Colours much 
more vivid than thofe of Air made thin between tW0 
Glaffes.' 

O B S. XXIII. 

Comparing the quantity of Light refkifted from the 
feveral Rings, I found that it was moft copious from 
the firft or inmoft, and in the exterior Rings be-^ 
came gradually lefs and lefs. Alfo the whitenefs of 
the firft Ring was ftronger than that refleded from 
thofe parts of the thinner medium which were with-^ 
out the Rings; as I could manifeftly perceive by view- 
ing at a diftance the Rings made by the two Obje£l:» 

E e 1 Glaffes^ 



^iC^ 



[28] 

Glaffesi or by comparing two Bubbles of Water blown 
at diftant times, in the firft of which the whitenefs 
appeared, which fucceeded all the Colours, and in: 
the other, the whitenefs which preceded them all. 

OB S. XXIV. 

When the two Objed-Glafles were lay'd upon one 
another, fo as to make the Rings of the Colours ap- 
pear, though with my naked Eye I could not difcern 
above 8 or 9 of thofe Rings, yet by viewing them 
through a Prifm I have feen a far greater multitude^ 
infomuch that I could number more than forty, befides 
many others, that were fo very fmall and clofe toge- 
ther, that I could not keep my Eye fteddy gr^jheiij^ 
feverally fo as to number them, but by their extend Hiav& 
fometimes eftimated them to be more than a hundred. 
And 1 believe the Experiment may be improved to the 
difcovery of far greater numbers. For they feem to 
be really unlimited, though vifible only fo far as they 
can be feparated by the refraftion, as I fhall hereafter 
explain. 

But It was but one fide of thefe Rings, namely, that 
towards which the refraftion was made, which by that 
refraSion was rendered diftinfl:, and the other fide be- 
came more confufed than when viewed by the naked 
Eye, infomuch that there I could not difcern above 
one or two, and fometimes none of thofe Rings, of 
which I could difcern eight or nine with my naked 
Eye. And their Segments or Arcs, which on the 
other fide appeared fo numerous, for the moft part 

exceeded 



[29 

exceeded not the third part of a Circko If the Re» 
fradion was very great, or the Prifm very diftant from 
the Objeft-Glaffes, the middle part of thofe Arcs be- 
came alfo confufed^ fo as to difappear and conftitute an 
even whitenefs, whilft on either fide their ends, as alfo 
the v^hole Arcs furtheft from the center, became di- 
ftinfter than before, appearing In the form as you fee. 
them defigned in the fifth Figure. Fig. 

The Arcs, where they feemed diftinftefl:, were only 
white and black fucceflively, without any other Co- 
lours intermixed. But in other places there appeared. 
Colours, whofe order was inverted' by the refraftion 
in fuch manner, that if I firfl: held the Prifm very near 
the Objeft-Glaffes , and then gradually removed^ it- 
further off towards my Eye, the Colours of the ad, 
5d, 4.th, and following Rings llirunk towards the. white 
that ejnerged between them , until they wholly va- 
nilhed into it at the middle of the Arcs, and after- 
wards emerged again in a contrary order. But at 
the ends of the Arcs they retained their order un- 
changed, 

I have fometimes fo lay'd one Obje6l:-Glafs upon 
the other, that to the naked Eye they have all over 
feemed uniformly white, without the leaft appearance 
of any of the coloured Rings ; and yet by viewing 
them through a Prifm, great multitudes of thofe Rings 
have difcovered themfelves. And in like manner plates 
of Mufcovy-glafs, and Bubbles of Glafs blown at a 
Lamp-furnace, which were not fo thin as to exhibit 
any Colours to the naked Eye, have through the Prifm 
exhibited a great variety of them ranged irregu-* 
larly up and down in the form of waves. And fo 

Bubbles 



Bubbles of Water, before they began to exhibit their 
Colours to the naked Eye or a By-ftander, have ap* 
peared through a Prifm, girded about with many pa- 
rallel and horizontal Rings ; to produce which efFedt, 
it was neceffary to hold the Prifm parallel, or very 
nearly parallel to the Horizon, and to difpofe it fo 
that the rays might be refrafted upwards. 



THE 



C 31 ] 

It ii 

SECOND BOOK 

OF 

O P T I 






i A xv jy X As 



Remarks u^onthe foregoing O^Jervations. 
of the 



'Aving given my Obfervations of thefe Colours^ 

before I make ufe of them to unfold the Caufes 

of the Colours of natural Bodies, it is convenient that 
by the fimpleft of tliem, fuch as are the id^ ^d, 4th5 
9th) lath, 1 8th,. aoth, and 14th , I firft explain the 
more expounded. And firft tofhewhowthe Colours 
in the fourth and eighteenth Obfervations are produ^ 
ced, let there be taken m any ri^ht line from the point 
Y, the lengths ¥ A, Y B, Y (^ YD, YE, YF, YG.Bg^ 
YHl^ in proportion to one another, as the Cube^roots 
©f the Squares of the numbers, {, y|, ^ j, ^) 1, 1, 1 5 w^here- 
by the lengths of a mufical Chord to found all the Notes 
is an Eighth are reprefented; tliat is, in the propor^ 
tion of the numbers 6500, 6814., 71 14, 7631, 8155,, 
8855, 9H3>. 1000.Q. And at the points A, B, C, D, 

E, F^ 



[32] 

E,F, G, H, let perpendiculars Aa^ B ^^ 15^6% be erefted, 
by whole intervals the extent of the feveral Colours 
fet underneath againft them, is to be reprefented. Then 
divide the line A a in fuch proportion as the numbers 
I, a, 5, 5, 6, 7, 9, lo, 1 1, ISJ'^r. fet at the points of divi- 
fion denote. And through thofe divifions from Y 
draw lines i I, i K, 3 L, 5 M, 6 N, 7 0^}^c, 

Now if A ci be luppofed to reprefent the thicknefs 
of any thin tranfparent Body , at which the outmoft 
violet is moft copioufly refleded in the firft Ring, or 
Series of Colours, then by the i gth Obfervation HK, 
will reprefent its thicknefs, at which the utmoft red 
is moft copioufly refleded in the fame Series. Alfo 
by the 5 th and 1 6th Obfervations, A 6 and HNwill 
denote the thickneffes at which thofe extreme Colours 
are moft copioufly refleded in the fecond Series, and 
A I o and H Q the thickneffes , at which they are 
moft copioufly reflefted in the tliird Series, and fo on. 
And the thicknefs at which any of the intermediate 
Colours are reflefted moft copioufly, wifl, according to 
the i4.th Obfervation, be defined by the diftance of the 
line A H from the intermediate parts of the lines 1 K, 
6N, loQ, }^c, againft which the names of thofe Co- 
lours are written below. 

But further, to define the latitude of thefe Colours in 
each Ring or Series, let A i defign the leaft thicknefs, 
and A 3 the greateft thicknefs, at which the extreme 
violet in the firft Series is refleded, and let H I, and 
H L, defign the like limits for the extreme red, and 
let the intermediate Colours be limited by the inter- 
mediate parts of the lines i I, and 3 L, againft which 
the oames of thofe Colours are written, and fo on : But 



C333 

yet with this caution, that the refle<9:ions be fuppofed 
ttrongeft at the intermediate Spaces, aK, 6N, loQ^JfTr, 
and from tiience to decreafe gradually towards thefe li- 
mits, 1 1, ? L, 5 M, 7 O, )3c. on either fide ; where 
you Jnuft not conceive them to be precifeiy limited, 
but to decay indefinitely. And whereas I have affigned 
the fame latitude to every Series, 1 did it, becaufe al- 
tiiough the Colours in the firfl: Series feem to be a little 
broader than the reft, by reafon of a ftronger reflexion 
there, yet that inequality is fo infenfible as fcarcely to 
be determined by Obfervation. 

Now according to this defcrlption, conceiving that 
the rays originally of feveral Colours are by turns re- 
fleded at the Spaces 1 1 L 5, 5 M O 7, 9 r R 1 1, l?r» 
atidtranfmitted at the Spaces AHIi,5LM5,70P9, 
b'r. it is eafy to know what Colour muft in the open Air 
be exhibited at any thicknefs of a tranfparent thin body. 
For if a Ruler be applied parallel to A H, at that di» 
ftance from it by which the thicknefs of the body is 
reprefented, the alternate Spaces 1 1 L 5, 5 M O 7,l5?'r, 
which it crofleth wall denote the reflefted original Co- 
lours, of which the Colour exhibited in the open Air 
is compounded. Thus if the conftitution of the green 
in the third Series of Colours be defired, apply the 
Ruler as you fee at ^ e^<P, and by its paffing through 
fome of the blue at -^ and yellow at o-, as well as through 
the green at ^, you may conclude that the green exhi^ 
bited at that thicknefs of the body is principally con» 
ftituted of original green, but not without a mixture 
of fome blue and yellow, 

■ Ff B¥ 



34 

By this means you may know how the Colours from 
the center of the Rings outward ought to fucceed in 
order as they were defcribed in the 4th and 18th Ob- 
fervations. For if you move the Ruler gradually from 
AH through all diftances, having paft over the firft 
fpace which denotes little or no reflexion to be made 
by thinned fubftances, it will firft arrive at i the violet, 
and then very quickly at the blue and green, which 
together with that violet compound blue, and then at 
the yellow and red , by whofe further addition that 
blue is converted into whitenefs, which whitenefs con* 
tinues during the tranfit of the edge of the Ruler from 
I to 5, and after that by the fucceffive deficience of 
its component Colours, turns firft to compound yellow^ 
and then to red, and laft of all the red ceafeth at L. 
Then begin the Colours of the fecond Series, which 
fucceed in order during the tranfit of the edge of the 
Ruler from 5 toO, and are more lively than before,, 
becaufe more expanded and fevered. And for the 
fame reafon, inftead of the former white there inter- 
cedes between the blue and yellow a mixture of orange, 
yellow, green, blue and indico, all which together ought 
to exhibit a dilute and imperfeft green. So the Co- 
lours of the third Series all fucceed in order ; firft, the 
violet, which a little interferes with the red of the fe- 
cond order, and is thereby inclined to a reddifti purple; 
then the blue and green , which are lefs mixed with 
other Colours, and confequently more lively than be- 
fore, efpecially the green : Then follows the yellow, 
fomeof which towards the green is diftind and good, but 
that part of it towards the fucceeding red, as alfo that 
led is mixed with the violet and blue of the fourth Se- 
ries, 



lies, whereby various degrees of red very much incli- 
ning to purple are compounded. This violet and blue, 
which fhould fucceed this red, being mixed with, and 
hidden in it, there fucceeds a green. And this at firft 
is much inclined to blue, but foon becomes a good 
green , the only unmixed and lively Colour in this 
fourth Series. For as it verges towards the yellow, it 
begins to interfere with the Colours of the fifth Series, 
by whofe mixture the fucceeding yellow and red are 
very much diluted and made dirty, efpecially the yel« 
low, which being the weaker Colour is fcarce able to 
Ihew it felf. After this the feveral Series interfere more 
and more, and their Colours become more and more 
intermixed, till after three or four more revolutions 
( in which the red and blue predominate by turns ) 
all forts of Colours are in all places pretty equally ben« 
ded, and compound an even whitenefs. 

And fince by the 15th Obfervation the rays indued 
with one Colour are tranfmitted, where thofe of ano- 
ther Colour are reiieded, the reafon of the Colours 
made by the tranfmitted Light in the 9th and 10th Ob- 
fervations is from hence evident. 

If not only the order and fpecies of thefe ColourSj 
but alio the precife thicknefs of the plate, or thin body 
at which they are exhibited, be defired in parts of an 
Inch, that may be. alfo obtained by affiftance of the 6tli 
or 1 6th Obfervations. For according to thofe Obferva^ 
tions the thicknefs of the thinned Air, which between 
two Glafles exhibited the moft luminous parts of the 
tirit lix Kmgs were 1-^3^5 iTSoSS"? TtHooSj i^aH^? itSSoo? vt^qSo psrts 01 
an Inch. Suppofe the Light reflefted moft copioufly 
at thefe thickneffes be the bright citrine yellow^ or con- 

Ff 1 fine 



C3^] 

fine of yellow and orange, and thefe thicknefles will 
be<JMj Gv, G^, Gp, G^. And this being known, it is 
eafy to determine what thicknefs of Air is reprefented' 
by G^, or by any other diftance of the ruler from 
AH. 

But further, fince by the i oth Obfervation the thick- 
nefs of Air was to the thicknefs of Water, which be- 
tween the fame GlajGTes exhibited the fame Colour, as 
4 to 5, and by the aith Obfervation the Colours of 
thin bodies are not varied by varying the ambient me- 
dium ; the thicknefs of a Bubble of Water, exhibiting 
any Colour, will be ^ of the thicknefs of Air producing 
the fame Colour. And fo according to the fame loth 
and ^ith Obfervations the thicknefs of a plate of 
Glafs, v^hofe refraftion of the mean refrangible i*ay, is 
meafured by the proportion of the Sines 31 to qo, 
may be f^ of the thicknefs of Air producing the fame 
Colours ; and the like of other mediums. 1 do not 
affirm, that this proportion of ao to 31, holds in all 
the rays ; for th^ Sines of other forts of rays have other 
proportions. But the differences of thofe proportions 
are fo little that 1 do not here confider them. Oil 
thefe Grounds 1 have compofed the following Table, 
wherein the thicknefs of Air, Water, and Glafs, at 
which each Colour is moft intenfe and fpecifick, is ex- 
preffed in parts of an Inch divided into Ten hundred 
thoufand equal parts. 



Tk 



[37 J 



The thichnefs of coloured Tlates and T articles of 



r Colours of the' 
firll Order, 



0f the.fecond Order, 



fVery Black 
Black 
Beginning of 

Black- 
Blue 
White 
Yellow- 
Orange 

^Redi 

^Violet 
Indico 
Blue 
Green 
i Yellow 
Orange 
Bright. Red 
LScarlet 

rpurple. 
Indico 
Blue 
Of the third'.Order, ^ Green 

Yellow. 
Red 
i^Bluifh Red 

Bluifh Green 
iGreen 

lYellowifh Green 
Red 

5Greenifli Blue 
iRed 

^Greenifh Blue 
^Red 

OfthefeventhOrderJGreeniih Blue 

'jRuddy White 



Of the fourth Order, 



Ofthe fifth Order 



Of the fixth Order, 



c 

Jir, 



•y 



Water, GUfs, 



i 1 1. 1 


1 


I 


8 


31 


I 


A 


a 


4 


31 


2 


li 


If 


2t 


If 


li^ 


5i 


3i 


3t 


l^ 


5t 


4i 


8 


6 


5i 


9 


^i 


5t 


lit 


U 


7t 


I2| 


pi 


8f. 


14 


loi 


9, 


Mi 


iif 


9^ 


i6f 


I2t 


lot 


i7t 


13 


III 


i8f 


i3i 


ii| 


191 


Hi 


I2f . 


21 


i5i 


l^is 


22Ti 


i^f 


i4t 


2?t 


i7ii 


1515 


^51 


i8fo 


i^i 


277 


20| 


'Z^ 


29 


2Ii 


i8'f 


32 


24 


20f 


H 


25t 


22 


35f 


26i 


22i 


3^ 


^7 


2|l 


4o| 


30* 


26 


46 


H» 


29t 


521 


19^^ 


34 _ 


44 


38 


65 


48i 


42. 


71 


534 


1 45? 


?7„ 


57i 


1 49t . 



Now 



Can 

Now if this Table be compared with the 6th Scheme, 
you will there fee the conftitution of each Colour, as 
to its Ingredients, or the original Colours of which it 
is compounded, and thence be enabled to judge of its 
intenfenefs or imperfedion ; which may fuffice in ex- 
plication of the 4th and 1 8th Obfervations, unlefs it 
be further defired to delineate the manner how the Co- 
lours appear, when the two Objed-Glafles are lay'd 
upon one another. To do which, let there be de- 
fcribed a large Arc of a Circle, and a ft r eight Line 
which may touch that Arc, and parallel to that Tan- 
gent feveral occult Lines, at fuch diftances from it, as 
the numbers fet againft the feveral Colours in the Table 
denote. For the Arc, and its Tangent, will reprefent 
the fuperficies of the Glaffes terminating the interjacent 
Air j and the places where the occult Lines cut the 
Arc will lliow at what diftances from the Center, or 
Point of contaft, each Colour is reflefted. 

There are alfo other ufes of this Table : For by its 
affiftance the thicknefs of the Bubble in the 1 9th Ob- 
fervatiDn was determined by the Colours which it ex- 
hibited. And fo the bignefs of the parts of natural 
Bodies may be conjedured by their Colours, as Oiall be 
hereafter Ihewn. Alfo, if two or more very thin plates 
be lay'd one upon another, fo as to compofe one plate 
equalling them all in thicknefs, the refulting Colour 
may be hereby determined e For inftance, Mr. Hook in 
^ his Miftrografbia obferves, that a faint yellow plate of 
^p;A^ ^p^^/Mufcov y-g lafs lay'd upon a blue one, conftituted a very 
Jeep purple. The yellow of the firft Order is a faint 
one^ and the thicknefs of the plate exhibiting it, ac- 
cortog to the Table is 4f , to which add 9, the thick- 
nefs 



^ 



C39] 

nels exhibiting blue of the fecond Order, and the fum 
will be 13', which is the thicknefs exhibiting the 
purple of the third Order. 

To explain, in the next place, the Circumftances of 
the ad and ^d Obfervations ; that is, how the Rings of 
the Colours may ( by turning the Prifms about their 
common Axis the contrary way to that expreffed in 
thofe Obfervations) be converted into white and black 
Rings,and afterwards into Rings of Colours again, the 
Colours of each Ring lying now in an inverted order; it 
muft be remembred, that thofe Rings of Colours are di- 
lated by the obliquation of the rays to the Air which 
intercedes the Glafles, and that according to the Table 
in the 7th Obfervation, their dilatation or increafe of 
their Diameter is moft manifeft and fpeedy when they 
are obliqueft. Now the rays of yellow being more re- 
fracted by the firft fuperficies of thefaid Air than thofe 
of red, are thereby made more oblique to the fecond fu^ 
perficies, at which they are reflefted to produce the co-- 
loured Rings, and confequently the yellow Circle in each 
Ring will be more dilated than the red; and the excefs of 
its dilatation will be fo much the greater, by how much 
the greater is the obliquity of the rays, until at laft it be- 
come of equal extent with the red of the fame Ring. And 
for the fame reafon the green, blue and violet, will be alio 
fo much dilated by the ftill greater obliquity of their 
rays, as to become all very nearly of equal extent with 
the red, that is, equally diftant from the center of the 
Rings. And then all the Colours of the fame Ring 
muft be coincident, and by their mixture exhibit a. 
white Ring. And thefe white Rings muft have black 
and dark Rings betw^een them ^ becaufe they do not 

fpread 



fpread and interfere with one another as before. And 
for that reafon alfo they muft become diftinfter and vi- 
fible to far greater Numbers. But yet the violet being 
obliqueft wilbbe fomething more dilated in proportion 
to its extent then the other Colours, and fo very apt to 
appear at the exterior verges of the white. 

Afterwards, by a greater obliquity of the rays, the 
violet and blue become more fenfibly dilated than the 
red and yellow, and fo being further removed from the 
center or the Rings, the Colours muft emerge out of the 
white in an order contrary to that which they had be- 
fore, the violet and blue at the exterior limos of each 
Ring,and the red and ydlow at the interior. And the vio- 
let, by reafon of the greateft obliquity of its rays, being 
in proportion moft of all expanded, will fooneft appear 
at the exterior limb of each white Ring, and become 
more confpicuous than the reft. And the feveral Series 
of Colours belonging to the feveral Rings , will, by 
their unfolding and fpreading, begin again to interfere, 
and thereby render the Rings lefs diftinft, and not vifi- 
ble to fo great numbers. 

If inftead of the Prifms the Objeil-glafles be made 
ufe of, the Rings which they exhibit become not white 
and diftindt by the obliquity of the Eye, by reafon that 
the rays in their paflage through that Air which inter- 
cedes the Glaffes are very nearly parallel to thofe Lines 
in which they were firft incident on the Glaffes, and con- 
fequently the rays indued with feveral Colours are not 
inclined one more than another to that Air, as it hap- 
pens in the Prifms. 

There is yet another circumftance of thefe Experiments 
to be confidered, and that is why the black and white 

Rings 



41 

Rings which when viewed at a diftance appear diftind^ 
fliould not only become confufed by viewing them near 
at hand , but alfo yield a violet Colour at both the 
edges of every white Ring. And the reafon is, that the 
rays which enter, the Eye at feveral parts of the Pupil, 
have feveral obliquities to the Glaffes, and thofe which 
are moft oblique^ if confidered apart, would reprefent 
the Rings bigger tlian thofe which are the leaft oblique. 
Whence the breadth of the perimeter of every white 
Ring is expanded outwards by the obliqueft rays^ 
and inwards by the leaft oblique. And this expanfion 
is fo much the greater by how much the greater is the 
difference of the obliquity ; that is, by how much the 
Pupil is wider, or the Eye nearer to the Glaffes. And 
the breadth of the violet muft be moft expanded, be- 
caufe the rays apt to excite a fenfation of that Colour 
are moft oblique to a fecond, or further fuperficies of 
the thin'd Air at which they are reflefted, and have 
alfo the greateft variation of obliquity , which makes 
that Colour fooneft €merge out pf the edges of the 
white. And as the breadth of every Ring is thus aoig-. 
mented, the dark intervals muft be.diminiftied, until 
the neighbouring Rings become continuous, and are 
blended, the exterior firft, and then thofe nearer the 
Center, fo that they can no longer be diftinguifli-d 
apart , but feem to conftitute an even and uniform 
whitenefs. 

^ Among all the Obfervations there is none accompa^ 
nied witn fo odd circumftances as the ^^th. Of thofe 
the principal are, that in thin plates^ which to the 
naked Eye feem of an even and uniform tranfparent 



[42]. 

whitenefs, without any terminations of (hadows^ the 
refraftion of a Prifm ftiouM make Rings af Colours ap- 
pear, whereas it ufually makes Objedts appear coloured 
only there where they are terminated with (hadows, or 
haveparts unequally luminous; and that it fhouldinake 
thofe Rings exceedingly diftinft and white, although 
it ufually renders Objeds confufed and coloured. The 
caufe of thefe things you will underftand by confidering^ 
that all the Rings of Colours are really in the plate^ 
when viewed with the naked Eye, although by reafon 
of the great breadth of their circumferences they fo 
much interfere and are blended together^that they {eem 
to conftitute an even whitenefs. But when the rays 
pafs through the Prifm to the Eye, the orbits of the 
ieveral Colours in every Ring are refrafted, fome more 
than others, according to their degrees of refi-angibility r 
By which means the Colours on one fide of the Ring 
f that is on one fide of its Center) become more unfolded 
md dilated, and thofe on the other fide more compli- 
cated and contrafted. And where by a due refradioB 
they are fo much contraded, that the fevral Rings be- 
come narrower than to interfere with one another, they 
muft appear diftinft, and alfo white^ if the conftituent 
Colours be fo much eontradedas to be wholly coincident. 
But^ oii the other fide, where the orbit of every Ring 
is made broader by the further unfolding of its Co- 
lours, it muft interfere more with other Rings than 
before, and fo become lefs diftinft. 

To explain this a little further, fuppofe the concen- 

•pl„ 7. ^^ Circles A V, and BX, reprefent the red and violet 

' of any order^ which, together with the intermediate 

Colours, 



[43] 

Colours, conftitute any one of thefe Rings. Now thefe 
being viewed through a Prifm, the violet Circle B X, 
will by a greater refraftion be further tranflated from 
its place than the red A V, and fo approach nearer to 
it on that ftde, towards which the refraftions are made. 
For inftance, if the red be tranflated to av^ the violet 
may be tranllated to b x, fo as to approach nearer to it 
at X than before, and if the red be further tranflated 
to a V, the violet may be fo much further tranflated to 
b X as to convene with it at x, and if the red be yet 
further tranflated to * ^\ the violet may be ftill fo much 
further tranflated to /3| as to pafs beyond it at I, and 
convene with it at e and/. And this being underftood 
not only of the red and violet, but of all the other in- 
termediate Colours, and alfo of every revolution of 
thofe Colours, you will eafily perceive how thofe of the 
fame revolution or order, by their nearnefs at xi/and 
'^ ^, and their coincidence at xv, ^ ^n<l/) ought to con-. 
flitute pretty diflinft Arcs of Circles, efpecially at xv^ 
or at ^and/, and that they will appear feverally at 
X z;, and at x v exhibit whitenefs by their coincidencey 
and again appear feveral at ^ I, but yet in a contrary 
order to that which they had before, and flill ittmh. 
beyond^ and/. But, on the other fide, ^t ai^ ab^ 
or a ^, thefe Colours muft become much more confu* 
fed by being dilated and fpread fo, as to interfere with 
thofe of other Orders. And the fame confufion will 
happen at ^^ i between e and/, if the refraction be very 
great, or the Prifm very diftant from theObjed-Glaffes : 
In which cafe no parts of the Rings will be feen, fave 
only two little Arcs at e and/, whofe diftance from one 

Gg a another^ 



44- 

another will be augmented by removing the Prlfm' 
ftill further from the Objeft-Glaffes : And thefe little 
Arcs muft be diftinftefl: and whiteft at their middle, and 
at their ends, where they begin to grow confuied they 
muft be coloured. And the Colours at one end of 
every Arc muft be in a contrary order to thofe at the 
other end, by reafon that they crofs in the interme^ 
diate white; namely their ends, which verge towards 
'^^, will be red and yellow on that fide next the Cen- 
ter, and blue and violet on the other fide. But their 
other ends which verge from '^ ^ will on the contrary 
be blue and violet on that fide towards the Center, and: 
on the other fide red and yellow. 

Now as all thefe things follow from the Properties^ 
©f Light by a mathematical way of reafoning, fo the 
truth of them may be manifefted by Experiments* For 
in a dark room, by viewing thefe Rings through a 
Prifm, by reflexion of the feveral prifmatique Colours, 
which an affiftant caufes to move to and fro upon ^ 
Wall or Paper from whence they are reflected, whilft^ 
the Speftator's Eye, thePrifm, and the Objeftr-Glaffes 
(as in the 13th Obfervation) are placed fteddy : the 
pofition of the Circles made fucceffively by the feveral 
Colours, will be found fuch, in refped: of one another^, 
as I have defcribed in the Figures aixv^ or abxvy; 
or aJgT, And by the fame method the truth of 
the Explications of other Obfervations may be exa- 
mined. 

By what hath been faid the like PhKnomlna of 
Water, and thin plates of Glafs may be underftood. 
But in fmall fragments of thofe plates, there is this^ 

further 



C45] 

further obfervable, that where they lye flat upon a 
Table and are turned about their Centers whilft they are 
viewed through a Prifm , they will in fome poftures 
exhibit waves of various Colours, and fome of them ex- 
hibit thefe waves in one or two pofitions only, but the 
Hioft of them do in all politions exhibit them, and make 
them for the moft part appear almoft all over the plates. 
The reafon is, that the fuperficies of fuch plates are not 
even, but have many cavities and fwellings, which how 
Ihallow foever do a little vary the thicknefs of the 
plate. For at the feveral fides of thofe cavities, for^^ 
the reafons newly defcribed, there ought to be produ^ 
ced waves in feveral poftures of the Prifm. Nowthough^ 
it be but fome very fmall, and narrower parts of the 
Glafs, by which thefe waves for the moft part are cau- 
fed, yet they may feem to extend themfelves over the 
whole Glafs, becaufefrom the narroweft of thofe parts 
there are Colours of feveral Orders that is of feveral 
Rings, confufedly refleded, which by refradion of the- 
Prifm are unfolded, feparated, and according to their 
degrees of refraftion, difperfed to feveral places, fo as to 
Gonftitute fo many feveral waves, as there were divers 
orders of Colours promifcuoufly refle£led from that 
part of the Glafs. 

Thefe are the principal Phaenomena of thin Plates^ 
or Bubbles, whofe explications depend on the pro- 
perties of Light, which I have heretofore delivered. 
And thefe you fee do neceffarily follow from them, and 
agree with them, even to their very leaft circumftances; 
and not only fo, but do very much tend to their proof. 
Thus, by the a^th Obfervation, it appears^ that the 

rays-..-. 



C4«] 

rays of feveral Colours made as well by thin Plates or 
Bubbles, as by refradtions of a Prifm, have feveral de- 
grees of refrangibility, v^hereby thofe of each order, 
which at their reflexion from the Plate or Bubble are 
intermixed with thofe of other orders, are feparated 
from them by refra£i:ion,and affociated together lb as to 
become vifible by themfelves like Arcs ot Circles. For 
if the rays were all alike refrangible, 'tis impoffible that 
the whitenefs, which to the naked fence appears uni- 
.form, fhould by refraction have its parts tranfpofed and 
ranged into thofe black and white Arcs. 

It appears alfo that the unequal refractions of dif- 
form rays proceed not from any contingent irregulari- 
ties ; fuch as are veins, an uneven polifh, or fortuitous 
poiition of the pores of Glafs , unequal and cafual mo- 
tions in the Air or ^ther ; the fpreading, breaking, or 
dividing the fame ray into many diverging parts, or 
the like. For, admitting any fuch irregularities, it would 
be impoflible for refractions to render thofe Rings fo 
very diftinCt , and well defined , as they do in the 
a^th Obfervation. It is neceflary therefore that eve- 
ry ray have its proper and conftant degree of refran- 
gibility connate with it,according to which its refraftion 
is ever juftly and regularly performed, and that feve- 
ral rays have feveral of thofe degrees. 

And what is faid of their refrangibility may be alfo 
underftood of their reflexibility, that is of their difpo- 
(itions to be reflected fome at a greater, and others at a 
lefs thicknefs, of thin Plates or Bubbles, namely, that 
thofe dlfpofitions are alfo connate with the rays, and 
immutable; as may appear by the 13th, 14th, and 

15th 



C47I 

15th Obfervations compared with the fourth and 
eighth. 

By the precedent Obfervations it appears alfo, that 
whitenefs is a diffimilar mixture of all Colours, and that 
Light is a mixture of rays indued with all thofe Co« 
lours. For confidering the multitude of the Rings of 
Colours, in the gd, nth and ^4.th Obfervations, it is 
manifeft that although in the 4th and 18th Obferva- 
tions there appear no more than eight or nine of thofe 
Rings, yet there are really a far greater number, which 
fo much interfere and mingle with one another, as after 
thofe eight or nine revolutions to dilute one another 
wholly, and conftitute an even and fenfibly uniform 
whitenefe. And confequently that whitenefs muft be 
allowed a mixture of all Colours, and the Light which 
conveys it to the Eye muft be a mixture of rays indued . 
with all thofe Colours. 

But further, by the a^th Obfervation , it appears^. 
that there is a conftant relation between Colours and 
Refrangibility, the moft refrangible rays being violet^ 
the leaft refrangible red, and thofe of intermediate Co- 
lours having proportionably intermediate degrees of re^ 
frangibility. And by the 1 3th, 14th and 1 5th Obfer- 
vations, compared with the 4.th or i8th, there appears 
to be the fame conftant relation between Colour and 
Reflexibility, the violet being in like circumftances re- 
flected at leaft thickneffes of any thin Plate or Bubble, 
the red at greateft thickneffes , and the intermediate 
Colours at intermediate thickneffes. Whence it fol- 
lows, that the colorifique difpofitions of rays are alfo 
connate with them and immutable, and by confequence 

that 



48] 

that all the produftions and appearances of Colours 
in the World are derived not from any phyfical change 
caufed in Light by refraction or reflexion, but only 
from the various mixtures or feparations of rays, by 
virtue of their different Refrangibility or Reflexibility, 
And in this refpeft the Science of Colours becomes a 
Speculation as truly mathematical as any other part of 
Optiques. I mean fo far as they depend on the nature 
of Light, and are not produced or altered by the power 
of imagination, or by (triking or prefling the Eyes. 



i 






Fig. 2. 



BooK,n. Plate,I. 









*!•• 



Zy ^ I' t s r ./pcnmlkih e^ f : d c 




Aj fg h ik I mmp ,jr s tir xf^i 







Book.n 



riarr.n. 



ex, $ y- 6 



FliTn- 



-y o 



f 



Fig. 6. 






B C 




D 


E 


F G 


k 


■*i-i 




5 


-^ 


jj 


t 


1 


^ 


>^ 


i 


'S 



H 




^^g-- 7- 




SECOND BOOK 

O P T I 






if A Jtv L JLJLx. 



Of the permanent Colours of natural Bodies j and the 
Analogy iet%<ueen them and the Colours of thin tranf^ 
parent Tlates. 

I Am now come to another part of this Defign, which 
is to confider how the Phasnomena of thin tranfpa- 
rent Plates ftand related to thofe of all other natural 
Bodies. Of thefe Bodies I have already told you that 
they appear of divers Colours, accordingly as they are 
difpofed to refled moft copioufly the rays originally 
indued with thofe Colours. But their Conftitutions^ 
whereby they refieft fome rays more copioufly than 
others, remains to be difcovered, and thefe I (hi '^ 
deavour to manifeft in the following Propofitions 



PROP. L 

T'hofefuperficieroftranf parent Bodies reflet thegreatefi 
quantity of Light ^ "which have the great eft ref racing poisuer; 
that is^ "which intercede mediums that differ moft m their 
refractive denfities. And in the confines of equally re- 
framing mediums there is no reflexion. ^ 
• The Analogy between reflexion and refraftlon will 
appear by confidering, that w^hen Light paffeth ob- 
liquely out of one medium into another which refrafts 
from the perpendicular, the greater is difference of 
their refractive denhty, the lels obliquity^ is requmte 
to caufe a ^tal reflexion. For as the Sines are which 
meafure the refradion, fo is the Sine of incidence at 
which the total reflexion begins, to the radius of the 
Circle, and confequently that incidence is leaft where 
there is the greateit difference of the Sines. Thus in the 
paffing of Light out of Water into Air, where the 
refraftion is meafured by the Ratio of the Sines 5 to 4^ 
the total reflexion begins when the Angle of incidence 
i% about 48 degrees 35 minutes. In paffing out ofGlafs 
iiito Air, where the refradion is meafured by the Ratio 
of the Sines qo to 51, the total reflexion begins when 
the Angle of incidence is 40 deg. 10 min. and fo in 
paffing out of cryftal, or more fl:rongly refra^Sing me- 
diums into Air, there is fl:ill a lefs obliquity requifite 
to caufe a total reflexion. Superficies therefore which 
refraft mofl: do foonefl: refleft all the Light which is in* 
cident on them, and fo muff be allowed mofl: ftrongly 
reflexive. 



Bur 



i 



But the truth of this Propofition will further appear 
by obferving , that in the fuperficies interceding two 
tranfparent mediums, fuch as are (Air, Water ,Oyl, Com- 
mon-Glafs, Cryftal, Metalline-Glafles , Ifland-Glaffes, 
white tranlparent Arfnick, Diamonds, If^c. ) the re- 
flexion is ftronger or weaker accordingly, as the fuper- 
ficies hath a greater or lefs refracting power. For in 
the confine of Air and Sal-gemm 'tis ftronger than in 
the confine of Air and Water, and ftill ftronger in the 
confine of Air andCommon'GlafsorCryftal,and ftronger 
in the confine of Air and a Diamond. If any of thefe,and 
fuch like tranfparent Solids, be immerged in Water, its 
reflexion becomes much weaker than before, and ftill 
weaker if they be immerged in the more ftrongly re-- 
framing Liquors of well-rectified oyl of Vitriol or fpirit 
of Turpentine. If Water be diftinguiflied into two parts, 
by any imaginary furface, the reflexion in the coejfine 
of thofe two parts is none at all. In the confine of Wa- 
ter and Ice 'tis very little, in that of Water and Oyl 'tis 
fomething greater, in that of Water and Sal-gemm ftill 
greater, and in that of Water and Glafs, or Cryftal, >dr 
other denfer fubftances ftill greater, accordingly = as thofe 
mediums diifer more or lefs in their refraSing powersi 
Hence in the confine of Common-Glafs and Gryftal, 
there ought to be a weak reflexion, and a ftronger re- 
flexion in the confine of Common and Metalline-Glafs, 
though I have not yet tried this. But, in the confine of 
two Glafles of equal denfity, there is not any fenfible re- 
flexion, as was (hewn in the firft Obfervation. And 
the fame may be underftood of the fuperficies interce- 
ding two Cryftals^ or two Liquors, or any other Sub** 
ftances in which no refraftion is caufed. So then the 

Hh 2 reafon 



[ 52 3 

reafon why uniform pellucid mediums, (fuch as Water, 
Glafs, or Cryftal) have no fenfible reflexion but ia 
their external fuperficies, where they are adjacent to 
other mediums of a different denfity , is becaufe ;^11 
their contiguous parts have one and the fame degree 
of denfity. 

PROP. II. 

The ieafl farts of almojl all natural Bodies are in fome 
meafure tranffarent : jind the ofacity of thofe Bodies 
arijeth from the multitude of reflexions caufed in their in^ 
ternal "Parts. ^ 

That this is fo has been obferved by others, and 
will eafily be granted by them that have been conver- 
fant with Mifcrofcopes. And it may be alfo tryed by 
applying any fubftance to a Hole through which fome 
Light is immitted into a dark room. For how opake 
foever that fubftance may feem in the open Air, it will 
by that means appear very manifeftly tranfparent, if 
it be of a fuflficient thinnefs. Only white metalline Bo- 
dies muft be excepted, which by reafon of their excef- 
five denfity feem to refleft almoft all the Light inci- 
dent on their firft fuperficies , unlefs by folution in 
menftruums they be reduced into very fmall particles^ 
and then they become tranfparent. 

PROP. IlL 

*'' Betisoeen the farts of ofake and coloured Bodies are 
many f faces ^ either emfty or reflenijhed^ ^with mediums 
of other denfities ; ^ Water ietmeen the tinging corfufcles 
'wherewith any Liquor k imfregnatedy Air between the 

' 7 a(j^ueo'Wi 



aqueom glohules that conftitute Clouds or Mifts | and for 
the mojl fart [faces void of ioth Air and Watery hut yet 
perhafs not ^wholly void of all f ub fiance^ het'wten the farts 
of hard Bodies. "^ 

The truth of this Is evinced by the two precedent 
Propofitions : For by the fecond Propofition there are 
many reflexions made by the internal parts of Bodies^ 
which, by the firft Propofition, would not happen if 
the parts of thofe Bodies were continued without any 
fuch inter ft ices between them, becaufe reflexions are 
caufed only in fuperficies, which intercede mediums of 
a differing denfity by Prop, i . 

But further, that this difcontinuity of parts is the 
principal caufe of the opacity of Bodies^ will appear by 
confidering, that opake fubftances become tranfparent 
by filling their pores with any fubftance of equal or al- 
moft equal denfity with their parts. Thus Paper dip- 
ped in Water or Oyl, the Oculm mundi Stone fteep'd in 
Water, Linnen-cloth oyled or varniftied,and many other 
fubftances foaked in fuch Liquors as will intimately 
pervade their little pores, become by that means more 
tranfparent than otherwife ; fo, on the contrary, the 
moft tranfparent fubftances may by evacuating their 
pores, or feparating their parts, be rendred fufficiently 
opake, as Salts or wet Paper, or the Oculm mundi Stone 
by being dried, Horn by being fcraped, Glafs by being 
reduced^ ,|qjDowder, or otherwife flawed, Turpen^ 
tinetBy !)eirfg ftirred about witfiT^Vater till they mix 
imperfeftly , and Water by being formed into many 
fmall Bubbles, either alone in the form of froth, or 
by ftiaking it together with Oyl of Turpentine , or 
with fome other convenient Liquor, with which it will 

not 



5+ ] 

not perfedly incorporate. And to the increafe of the 
opacity of thefe Bodies it conduces fomething, that by 
the agth Obfervation the reflexions of very thin trans- 
parent fubftances are confiderably {Ironger than thofe 
inade by the fame fubftances of a greater thicknefs. 

PROP. IV. 

T'he farts . of Bodies and their Inter flic es mufl not he 
lefs than offome definite hignejs^ to render them opake and 
coloured. 

For the opakeft Bodies, if their parts be fubtily 
divided, ( as Metals by being diflblved in acid men- 
ftruums, %c.) become perfedly tranfparent. And you 
may alfo remember, that in the eighth Obfervation 
there was no fenfible reflexion at the fuperficies of 
the Objeft-Glafles where they were very near one 
another, though they did not abfolutely touch. And 
in the i yth Obfervation the reflexion of the Water-bubble 
where it became thinneft was almoft in fenfible, fo as 
to caiife very black Spots to appear on the top of the 
Bubble by the want of refleded Light. 
■ On thefe grounds I perceive it is that Water, Salt, 
Glafs, Stones, and fuch like fubftances, are tranfparent. 
For, upon divers conliderations, they feem to be as full 
of pores or interftices between their parts as other Bo- 
dies are, but yet their parts and interftices to be too 
fmall to caufe reflexions in their common furfaces. 



PROP. 



1 55 ] 



PROP, V. 

T^he tranffarent farts of Bodies according ta their fe^ 
veral fizes rauji rejleB ra'js of one Colour^ and tranfmit 
thofe of another^ on the fame grounds tha.t thin plates or 
Bubbles do refieH or tranfmit thofe rays. j4nd this I take 
to be the ground of all their Colours. 

For if a thin'd or plated Body, which being of an 
even thicknefs, appears all over of one uniform Co- 
lour, fhould be llit into threds, or broken into frag- 
ments, of the fame thicknefs with the plate ; I fee no 
reafon why every thred or fragment fhould not keep its 
Colour, and by confequence why a heap of thofe threds 
or fragments ftiould not conftitute a mafs or powder of 
the lame Colour, which the plate exhibited before it 
was broken. And the parts of all natural Bodies being 
like fo many fragments of a Plate, muft on the fame 
grounds exhibit the fame Colours. 

Now that they do fo, will appear by the afftnity of 
their properties. The finely coloured Feathers of fome 
Birds, and particularly thofe of Peacocks Tails, do in 
the very fame part of the Feather appear of feveral Co» 
lours in feveral pofitions of the Eye, after the very fame 
manner that thin Plates were found to do in the 7th 
and 19th Obfervations, and therefore arife from the 
thinnefs of the tranfparent parts of the Feathers | that 
is, from the flendernefs of the very fine Hairs, or CafiUa^ 
mentaj, which grow out of the fides of the groffer late- 
ral branches or fibres of thofe FeatherSo And to the 
lame purpofe it is, that the Webs of fome Spiders by 

beins 



being fpun very fine have appeared coloured, as fome 
have obferved^ and that the coloured fibres of fome filks 
by varying the pofition of the Eye do vary their Co- 
lour. Alfo the Colours of filks, cloths, and other fub- 
ftances, which Water or Oyl can intimately penetrate, 
become more faint and obfcure by being immerged in 
thofe liquors, and recover their vigor again by being 
dried, much after the manner declared of thin Bodies 
in the loth and nth Obfervations. Leaf-gold, fome 
forts of painted Glafs, the infufion of Lignum Mefhru 
t'tcum^ and fome other fubftances reflect one Colour, 
and tranfmit another, like thin Bodies in the 9th and 
aoth Obfervations. And fome of thofe coloured pow- 
ders which Painters ufe, may have their Colours a little 
changed, by being very elaborately and finely ground. 
Where I fee not what can be juftly pretended for thofe 
changes, befides the breaking of their parts into lefs 
parts by that contrition after the fame manner that the 
Colour of a thin Plate is changed by varying its thick- 
nefs. For which reafon alfo it is that the coloured flowers 
of Plants and Vegitables by being bruifed ufually be- 
come more tranfparent than before, or at leaft in fome 
degree or other change their Colours. Nor is it much 
lefs to my purpofe, that by mixing divers liquors very 
odd and remarquable productions and changes of Co« 
lours may be effefted, of which no caufe can be more 
obvious and rational than that the faline corpufcles of 
one liquor do varioufly aft upon or unite with the 
tinging corpufcles of another, fo as to make them fwell, 
or Ihrink (whereby not only their bulk but their den- 
fity alfo may be changed ) or to divide them into 
fmaller corpufcles, (whereby a coloured liquor may be- 
come 



C57] 

come tranfparent) or to make many of them aflbciate 
into one clufter, whereby two tranfparent liquors may 
compofe a coloured one. For we fee how apt thofe 
faline menftruums are to penetrate and diffolve fub- 
ftances to which they are applied, and fome of them 
to precipitate what others diffolveo In like manner, if 
we confider the various Phaenomena of the Atmofphaere, 
we may obferve, that when Vapors are firft raifed, they 
hinder not the tranfparency of the Air, being divided 
into parts too fmall to caufe any reflexion in their fuper- 
ficies. But when in order to compofe drops of rain they 
begin to coalefce and conflitute globules of all inter- 
mediate fizes, thofe globules when they become of a 
convenient fize to refled fome Colours and tranfmit 
others, may conftitute Clouds of various Colours accor- 
ding to their fizes. And I fee not what can be ratio- 
nally conceived in fo tranfparent a fubftance as Water for 
the produftion of thefe Colours, befides the various 
fizes of its fluid and globuler parcels^ 

P R O R VL 

The farts of Bodies on "which their Colours defend^ 
are denjer than the medium , "which fervades their in^ 
terjiices, / 

This will appear by confidering, that the Colour of 
a Body depends not only on the rays which are inci- 
dent perpendicularly on its parts, but on thofe alf© 
which are incident at all other Angles^ And that ac- 
cording to the 7th Obfervation, a very little variation 
of obliquity will change the refleded Colour where the 
thin body or fmall particle is rarer than the ambient 

I i medium* 



58 

inedium,. infomuch that fuch a fmall particle will at di- 
verily oblique incidences refled all forts of Colours, "in 
fo great a variety that the Colour relulting from them 
all, confufedly reflected from a heap of fuch particles, 
muft rather be a white or grey than any other Colour, 
or at beft it muft be but a very imperfeft and dirty Co- 
lour. Whereas if the thin body or flnall particle be 
much denfer than the ambient medium, the Colours 
according to the 1 9th Obfervation are fo little changed 
by the variation of obliquity, that the rays which are 
reflefted leaft obliquely may predominate over the reft 
fo much as to caufe a heap of fuch particles to appear 
very intenfly of their Colour. 

It conduces alfo fomething to the confirmation of this 
Propolition, that, according to the aith Obfervation, 
the Colours exhibited by the denfer thin body within 
the rarer, are more brifque than thofe exhibited by the 
rarer within the denfer. 

P R OP. VI I. 

The hignejs of the component farts of natural Bodies 
mWj he conjeBured i>j their Colours. 

For fince the parts of thefe Bodies by Prop. 5. do 
moft probably exhibit the fame Colours with a Plate of 
equal thicknefs, provided they have the fame refractive 
denfity ; and fince their parts feem for the moft part to 
have much the fame denfity with Water or Glafs, as 
by many circumftances is obvious to colled: ; to deter- 
mine the fizes of thole parts you need only have recourfe 
to the precedent Tables, in which the thicknefs of Wa- 
ter ojj Glals exhibiting any Colour is expreffed. Thus 

if 



if it be defired to know the Diameter of a corpufcle, 
which being of equal denfity with Glafs fhall refleft 
green of the third order ; the number 1 6\ lliews it to 
be ^^^ parts of an Inch. 

lOCOOO 

The greateft difficulty is here to know of what order 
the Colour of any Body is. And for this end we muft 
have recourfe to the 4.th and 1 8th Obfervations, from 
whence may be collected thefe particulars. 

Scarlets J and other reds^ oranges and 'jeUo'ws^ if they 
be pure and intenfe are moft probably of the fecond or> 
der. Thofe of the firft and third order alfo may be 
pretty^ good, only the yellow of the firft order is faint, 
and the orange and red of the third order have a great 
mixture of violet and blue. 

There may be good greens of the fourth or4er^ but 
the pureft are of the third. And of this ordex the green 
of all vegitables feem to be, partly by reafon of the in- 
tenfenefs of their Colours , and partly becaufe when 
they wither forne of them turn to a greenlfli yellow, 
and others to a more perfect yellow or orange, or per^ 
haps to red, paffing firft through all the aforefaid in=> 
termediate Colours. Which changes feem to be efffe£ted 
by the exhaling of the moifture which may leave the 
tinging corpuCcles more denfe, and fomething augmen- 
ted by the accretion of the oyly and earthy part of 
that moifture. Now the green without doubt is of the 
lame order with thofe Colours into which it changeth, 
becaufe the changes are gradual, and thofe Colours, 
though ufually not very full, yet are often too full and 
lively to be of the fourth order. 

. I i 2 Blues 



[do] 

Blues and fur fies maybe either of the fecond or third 
order, but the beft are of the third. Thus the Colour 
of violets feems to be of that order, becaufe their Syrup 
by acid Liquors turns red, and by urinous and alcali- 
zale turns green. For fince it is of the nature of Acids 
to diffolve or attenuate, and of Alcalies to precipitate 
or incraflate, if the purple Colour of the Syrup was of 
the fecond order, an acid Liquor by attenuating its ting- 
ing corpufcles would change it to a red of the firft 
order, and an Alcaly by incralTating them would change 
it to a green of the fecond order ; which red and green, 
efpecially the green, feem too imperfe£t to be the Co- 
lours produced by thefe changes. But if the laid purple 
be fuppofed of the third order, its change to red of the 
fecond, and green of the third, may without any in- 
convenience be allowed. 

If there be found any Body of a deeper and lefs red- 
difli purple than that of the violets, its Colour moft' 
probably is of the fecond order. But yet their being 
no Body commonly known whofe Colour is conftantly 
more deep than theirs, I have made ufe of their name to 
denote the deepeft and leaft reddifh purples, fuch as 
manifeftly tranfcend their Colour in purity. 

The Hue of the firft order , though very faint and 
little, may poffibly be the Colour of fome fubftances ; 
and particularly the azure Colour of the Skys feems to 
be of this order. For all vapours when they begin to 
condenfe and coalefce into fmall parcels, become firft of 
that bignefs whereby fuch an Azure muft be reflected 
before they can conftitute Clouds of other Colours. And 
fo this being the firft Colour which vapors begin to 
reiieft, it ought to be the Colour of the tineft and moft 

tranf- 



tranfparent Skys in which vapors are not arrived to that 
groihefs requifite to refled other Colours, as we find it 
is by experience. 

TVbitenefs^ if moft intenfe and luminous, is that of the 
firft order, if lefs ftrong and luminous a mixtui'e of the 
Colours of feveral orders. Of this laft kind is the 
whitenefs of Froth, Paper, Linnen, and moft white fub- 
ftances ; of the former I reckon that of white metals to 
be. For whilft the denfeft of metals. Gold, if foliated 
is tranfparent, and all metals become tranfparent if 
diffolved in menftruums or vitrified, the opacity of 
white metals arifeth not from their denfity alone. They 
being lefs denfe than Gold would be more tranfparent 
than it, did not fome other caufe concur with their den- 
fity to make them opake. And this caufe I take to be 
fuch a bignefs of their particles as fits them to refle£t 
the white of the firft order. For if they be of other 
thicknelTes they may refleft other Colours,, as is mani- 
feft by the Colours which appear upon hot Steel in tem^ 
pcring it, and fometimes upon the furface of melted 
metals in the Skin or Scoria which arifes upon them in 
their cooling. And as the white of the firft order is 
the ftrongeft which can be made by Plates of tranfparent 
fubftances, fo it ought to be ftronger in the denfer fub- 
ftances of metals than in the rarer of Air, Water and 
Glafs.. Nor do I fee but that metallic fubftances -of fuch. 
a thicknefs as may fit them to refled the white of the 
firft order, may, by reafon of their great denfity (accor- 
ding to the tenour of the firft of thefe Propofitions) res- 
iled: all the Light incident upon them, and fo be as 
opake and fplendent as its poinble for any Body to be. 
Gold, or Copper mixed with lefs than h^lf their weight 

q£ 



I 62 J 

of Silver, or Tin, or Regulus of Antimony, in fufion 
or amalgamed with a very little Mercury become white; 
which Ihews both that the particles of white metals 
have much more fuperficies, and fo are fmaller, than 
thofe of Gold and Copper, and alfo that they are lb 
opake as not to fuifer the particles of Gold or Copper to 
fhine through them. Now it is fcarce to be doubted, 
but that the Colours of Gold and Copper are of the fe- 
eond or third order, and therefore the particles of white 
metals cannot be much bigger than is requifite to make 
them refled the white of the firft order. The volati- 
lity of Mercury argues that they are not much bigger, 
nor may they be much lefs, leaft they lofe their opacity, 
and become either tranfparent as they do when attenua- 
ted by vitrification, or by folution in menftruums, or 
black as they do when ground fmaller, by rubbing Sil- 
ver,or Tin, or Lead, upon other fubftances to draw black 
Lines. The firit and only Colour which white metals 
take by grinding their particles fmaller is black, and 
therefore their white ought to be that which borders 
upon the black Spot in the center of the Rings of Co- 
lours, that is, the white of the firft order. But if you 
would hence gather the bignefs of metallic particles, 
you muft allow for their denfity. For were Mercury 
tranfparent, its denfity is fuch that the Sine of inci- 
dence upon it (by my computation) w^ould be to the 
fine of its refraftion, as 71 to ao, or 7 to o>. And 
therefore the thickneis of its particles, that they may 
exhibit the fiime Colours with thofe of Bubbles of War 
ter, ought to be lefs than the thicknefs of the Skin of 
thofe Bubbles in the proportion of 2 to 7. Whence 
it;s poffible that the particles of Mercury may be as little 

as 



C ^3 3 

as the particles of fome tranfparent and volatile fluids, 
and yet retled the white of the firft order. 

Laftly, for the production of hlack^ the corpufcles 
muft be lefs than any of thofe which exhibit Colours. 
For at all greater fizes there is too much Light refle-' 
ded to conftitute this Colour. But if they be fuppo- 
fed a little lefs than is requifite to refle£t the white and 
very faint blue of the hrft order, they will, according 
to the 4th, 8th, 17th and i8th Obfervations, refleft 
fo very little as to appear intenfly black, and yet may 
perhaps variouily refraft it to and fro within them* 
felves fo long, until it happen to be ftifled and loft, 
by which means they will appear black in all pofitions 
of the Eye without any tranfparency. And from hence 
may be underftood why Fire , and the more fubtile 
diffolver Putrefadion, by dividing the particles of fub- 
ftances, turn them to black, why fmall quantities of 
black fubftances impart their Colour very freely and in- 
tenfly to other fubflances to which they are applied ; 
the minute particles of thefe, by reafon of their very 
great number, eafily overfpreading the grofs particles 
of others ; vdiy Glafs ground very elaborately with 
Sand on a copper Plate, 'till it be well poliflied, makes 
the Sand, together with what is worn off from the Glafs 
and Copper^ become very black : why black fubftances 
do fooneft of all others become hot in the Sun's Light 
and burn, (which effed: may proceed partly from the 
multitude of refractions in a little room, and partly 
from the eafy commotiofii of fo very fmall corpufcles;) 
and why blacks are ufually a little inclined to a bluifh 
Colour. For that they are fo may be feen by illumina- 
ting white Paper by Light retledted from black fub* 

ftances,- 



d4] 

ftances. For the Paper will ufually appear of a bluifli 
white ; and the reafon is, that black borders on the 
obfcure blue of the firft order defcribed in the i8th 
Obfervation, and therefore reflefts more rays of that 
Colour than of any other. 

In thefe Defcriptions I have been the more particu- 
lar, becaufe it is not impoffible but that Mifcrofcopes 
may at length be improved to the difcovery of the 
particles of Bodies on which their Colours depend, if 
they are not already in fome meafure arrived to that de- 
gree of perfection. For if thofe Inftruments are or can 
be fo far improved as with fufficient diftindnefs^ to re- 
prefent Objeds five or fix hundred times biggerttlian 
at a Foot diftance they appear to our naked Eyes, I 
fhould hope that we might be able to difcover fome of 
the greateft of thofe corpufcles. And by one that would 
magnify three or four thoufand times perhaps they 
might all be difcovered, but thofe which produce black- 
nefs. In the mean while I fee nothing material in this 
Difcourfe that may rationally be doubted of excepting 
liiis Pofition, That tranfparent corpufcles of the fame 
thicknefs and denfity with a Plate, do exhibit the fa#e 
Colour. And this I would have underftood not with- 
out fome latitude, as well becaufe thofe corpufcles may 
be of irregular Figures, and many rays muft be oblique- 
ly incident on them, and fo have a fhorter way through 
them than the length of their Diameters, as becaufe the 
ftraitnefs of the medium pent in on all fides within fuch 
corpufcles may a little alter its motions or other qua- 
lities on which the reflexion depends. But yet I can- 
not much fufpeft the laft, becaufe I have obferved of 
fome fmall Plates of Mufcovy-Glafs which were of an 

even 



even thicknefs, that through a Mifcrofcope they have 
appeared of the fame Colour at their edges and cor- 
ners where the included medium w^as terminated, which 
they appeared of in other places. However it will add 
much to our fatisfaftion, if thofe corpufcles could be dif- 
covered with Mifcrofcopes ; which if we fhall at length 
attain to, I fear it will be the utmoft improvement of 
this fenfe. For it feems impoffible to fee the more fe- 
cret and noble works of nature within the corpufcles 
by reafon of their tranfparency. 

P R O R VIIL 

T^he caufe of Reflexion is not the imfinging of Light on 
the folid or im^ervtom farts of Bodies ^ as is commonly ie* 
lieved. 

This will appear by the following Confiderations» 
Firft, That in the paffage of Light out of Glafs into 
Air there is a reflexion as flrong as in its paffage out of 
Air into Glafs, or rather a little ftronger, and by many 
degrees ftronger than in its paffage out of Glafs into 
Water. And it feems not probable that Air fhould have 
more reflefting parts than Water or Glafs. But if that 
Ihould poffibly be fuppofed, yet it will avail nothing | 
for the reflexion is as ftrong or fl:ronger when the Air is 
drawn away from the Glafs, (fuppofe in the Air-pump 
invented by Mr. Boyle ) as when it is adjacent to it. 
Secondly, If Light in its paffage out of Glafs into Air 
be incident more obliquely than at an Angle of 40 or 
41 degrees it is wholly reflected, if lefs obliquely it is 
in great meafure tranfmitted. Now it is not to be ima- 
gined that Light at one degree of obliquity fliould meet 

K k with 



with pores enough in the Air to tranfmit the greater 
part of it, and at another degree of obUquity fhould 
meet with nothing but parts to refleft it wholly, efpe^ 
daily conlidering that in its paffage out of Air into 
Glafs , how oblique foever be its incidence , it finds 
pores enough in the Glafs to tranfmit the greateft part 
of it. If any Man fuppofe that it is not refleded by the 
Air,- but by the outmoft fuperficial parts of the Glafs^ 
there is ftill the fame difficulty : Beiides, that fuch a 
Suppofition is unintelligible, and will alfo appear to be 
falfe by applying Water behind fome part of the Glafs 
inftead of Air. For fo in a convenient obliquity of the 
rays fuppofe of 45 or 46 degrees, at which they are all 
refieded where the Air is adjacent to the Glafs, they 
fliall be in great meafure tranfmitted where the Water 
is adjacent "to it; which argues, that their refkxion 
or. tranfmiffion depends on the conftitution of the Air 
and Water behind the Glafs, and not on the ftriking 
off the rays upon the parts of the Glafs. Thirdly, If 
the Colours made by a Prifm placed at the entrance of 
a beam of Light into a darkened room be fucceffively 
caft on a fecond Prifm placed, at a greater diftance from 
the former, in fach manner that they are all alike inci- 
dent upon it, the fecond Prifm may be fo inclined to 
the incident rays, that thofe which are of a blue Colour 
fhall be all reflefted by it, and yet thofe of a red Colour 
pretty copioufly tranfmitted. Now if the reflexion be 
caufed by the parts of Air or Glafs, I would ask, why 
at the fame obliquity of incidence the blue fhould whol- 
ly impinge on thofe parts fo as to be all refleded, and 
yet the red find pores enough to be in great meafure 
tranfmitted. Fourthly, where two Glalles touch one 

another^ 



another, there is no fenfible reflexion as was declared 
in the firft Obfervation; and yet I fee no reafon why 
the rays fhould not impinge on the parts of Glafs as 
much when contiguous to other Glafs as when con- 
tiguous to Air. Fifthly, When the top of a Water- 
bubble (in the i yth Obfervation) by the continual fub- 
fiding and exhaling of the Water grew very thin, there 
was fuch a little and almoft infenfible quantity of Light 
refle£led from it, that it appeared intently black ; where- 
as round about that black Spot, where the Water was 
thicker, the reflexion was lb ftrong as to make the 
Water feem very white. Nor is it only at the leaft 
thicknefs of thin Plates or Bubbles, that there is no 
manifefl: reflexion, but at many other thicknelTes con- 
tinually greater and greater. For in the 1 5 th Obfer- 
vation the rays of the fame Colour were by turns tranf- 
mitted at one thicknefs^ and reflected at another thick- 
nefs, for an indeterminate number of fucceflions. And 
yet in the fuperficies of the thinned Body, w^here it is 
of any one thicknefs, there are as many parts for the 
rays to impinge on, as where it is of any other thick- 
nefs. Sixthly, If reflexion were caufed by the parts of 
reflecting Bodies, it would be impoflible for thin Plates 
or Bubbles at the fame place to reflect the rays of one 
Colour and tranfmit thofe of another, as they do accor^ 
ding to the 13th and 15th Obfervations. For it is 
not to be imagined that at one place the rays which 
for infl:ance exhibit a blue Colour, ftiould have the for- 
tune to dafli upon the parts, and thofe which exhibit 
a red to hit upon the pores of the Body ; and then at 
another place, where the Body is either a little thicker, 
or a Uttle thinner, that on the contrary the blue fliould 

K k a * hit 



d8] 

hit upon its pores, and the red upon its parts, Laftly^ 
were the rays of Light reflefted by impinging on the 
folid parts of Bodies, their reflexions from poliflied Bo- 
dies could not be fo regular as they are. For in po- 
lilTiing Glafs with Sand, Putty or Tripoly, it is not to 
be imagined that thofe fubftances can by grating and 
fretting the Glafs bring all its leaft particles to an ac- 
curate polifh ; fo that all their furfaces fhall be truly 
plain or truly fpherical^ and look all the fame way, fo 
as together to compofe one even furface. The fmaller 
the particles of thole fubftances are, the fmaller will 
be the fcratches by which they continually fret and wear 
away the Glafs until it be polifhed, but be they never 
fo fmall they can wear away the Glafs no otherwife 
than by grating and fcratching it , and breaking the 
proturberances , and therefore polifh it no otherwife 
than by bringing its roughnefs to a very fine Grain, fo 
that the fcratches and frettings of the furface become 
too fmall to be vifible* And therefore if Light were 
refleded by impinging upon the folid parts of the Glafs^ 
it would be Icattered as much by the moft poliflied 
Glafs as by the rougheft. So then it remains a Pro- 
bkm, how Glafs poliflied by fretting fubftances can re- 
fled Light fo regularly as it does. And this Problem 
is fcarce otherwife to be folved than by faying, that 
the reflexion of a ray is efFeded, not by a Angle point of 
the refleding Body, but by fome power of the Body 
which is evenly diffufed aU over its furface, and. by 
which it ads upon the ray without immediate contad. 
For that the parts of Bodies do ad upon Light at a di- 
ftance fliall be fliewn hereafter^ 

Now 



Now if Light be reflefted not by impinging on the 
folid parts of Bodies, but by fome other principle ; its 
probable that as many of its rays as impinge on the 
folid parts of Bodies are not reflefted but ftifled and 
loft in the Bodies. For otherwife we muft allow two 
forts of reflexions. Should all the rays be reflected which 
impinge on the internal parts of clear Water or Cryftal, 
thofe fubftances would rather have a cloudy Colour 
than a clear tranfparency. To make Bodies look black, 
its neceflary that many rays be ftopt, retained and loft 
in them, and it feems not probable that any rays can 
be ftopt and ftifled in them which do not impinge on 
their parts. 

And hence we may underftand that Bodies are much 
more rare and porous than is commonly believed. Wa- 
ter is 1 9^ times lighter, and by confequence 1 9 times 
rarer than Gold , and Gold is fo rare as very readily 
and without the leaft oppofition to tranfmit the mag- 
netick. EfHuvia, and eafily to admit Quick-filver into 
its pores, and to let Water pafs through it. For a con- 
cave Sphere of Gold filled, with Water, and fodered up,' 
has upon prefling^ the Sphere with great force, let the 
Water fqueeze througli it, and ftand. all over its out- 
fide in multitudes of fmall Drops, like dew, without 
burfting or cracking the Body of the Gold as I have 
been informed by an Eye^witnefs. From all which we 
may conclude, that Gold has more pores than folid 
parts, and by confequence that Water has above forty- 
times more pores than parts. And he that fhali find out 
anHypothefis, by which Water may be fo rare, and yet 
not be capable of compreflion by force, may doubtlefs 
by the fame Hypothefis make Gold and Water, and all 

other 



C7o] 

Other Bodies as much rarer as he pleafes, fo that Light 
may find a ready paflage through tranfparent fub- ,, 
ftances. ^d-. aJirU^^ ^ ^n^-pslkj <^^^ki>i4^l^ti,>6die.^ "^h^x^S 

P R O P. IX, 

^Bodies refieB and refraB Light iy one and the fame 
fo^wer varioujly exercijed in variom circumflances, v 

This appears by feveral Confiderations. Firft, Be^ 
caufe when Light goes out of Glafs into Air, as ob- 
liquely as it can poffibly do, if its incidence be made 
ftill more oblique , it becomes totally refleded. For 
the power of the Glafs after it has refracted the Light 
as obliquely as is poffible if the incidence be ftill made 
more oblique, becomes too ftrong to let any of its rays 
go through, and by confequence caufes total reflexions. 
Secondly , Becaufe Light is alternately reflefted and 
tranfmitted by thin Plates of Glafs for many fucceflions 
accordingly , as the thicknefs of the Plate increafes 
in an arithmetical Progreflion. For here the thicknefs 
of the Glafs determines whether that power by which 
Glafs afts upon Light fhall caufe it to be reflefted, or 
fuifer it to be tranfmitted. And, Thirdly, becaufe thofe 
furfaces of tranfparent Bodies which have the greateft 
refrafting power, refleft the greateft quantity of Light, 
as was fhewed in the firft Propofition. 

PROP. X. 

s If Light he fvoifter in Bodies than in Vacuo in the 
ffofcrtion of the Sines 'which meafure the refraction of the 
B^dies^ the forces of the Bodies to rejleB and refraB Light ^ 



are 



[71] 

are ver^ nearly i^r of onioned to the denfities of the jame 
Bodies J excepting that undiuom and fulfhureom Bodies re^ 
fra^ more than others of this fame denfit'j . ^ ' 

Let A B reprefent the refrafting plane furfacc of any '4/rA9^//i?4>f ^J^ 
Body/ and IC a ray incident very obliquely upon the '?^- ^^^ 




Body in C, fo that the Angle A CI may be infinitely 
little^ and let C R be the refracted ray. From a given 
point B perpendicular to the refracting furface ere£t 
B R meeting w^ith the refradied ray C R in R, and if 
CR reprefent the motion of the refracted ray, and this^ 
motion be diftinguilhed into two motions CB and BR^ 
whereof CB is a parallel to the refracting plane, and 
BR perpendicular to it : CB fhall reprefent the motion 
of the incident ray, and B R the motion generated by 
the refraction, as Opticians have of late explained. 

Now if any body or thing in moving through any 
fpace of a giving breadth terminated on both fides by 
two parallel plains, be urged forward in all parts of 
that fpace by forces tending direCtly forwards towards 
the lafl: plain , and before its incidence on the firil 
plane, had no motion towards it, or but an infinitiy 
little one ; and if the forces in all parts of that fpace^ 
between the planes be at equal difl:ances from the planes 
equal to one another, but at feveral difl:ances be bigger 
or lefs in any given proportion, the motion generated 
by the forces in the whole paflage of the body or thing 

tlirough. 



[72] 

through that fpace (hall be in a fubduplicate proportion 
of the forces, as Mathematicians will eafily underftand. 
And therefore if the fpace of aftivity of the refradling 
fuperficies of the Body be confidered as fuch a fpace, 
the motion of the ray generated by the refrading force 
of the Body , during its paflage through that fpace 
that is the motion BR muft be in a fubduplicate 
proportion of that refra61:ing force : I fay therefore that 
the fquare of the Line BR, and by confequence the 
refracting force of the Body is very nearly as the den- 
fity of the fame Body. For this will appear by the fol- 
lowingTable, wherein the proportion of the Sines which 
meafure the refraxions of feveral Bodies, the fquare 
of BR fuppofing CB an unite, the denfities of the 
Bodies eftimated by their fpecifick gravities, and their 
refraftive power in refpeft of their denfities are fet 
down in feveral Columns. 



The 



[73] 



The refrading Bodies. 



The Proportion 
of the Sines of 
incidence and 
refraction of 
yellow Light, 



A Pfeudo-Topazius, be- 
ing a natural,pellucid, 
brittle, hairy Stone, of 
a yellow Colour 

Air 

Glafs of Antimony 

A Selenitis 

Glafs vulgar 

Cryftal of the Rock 

Ifland Cryflal 

Sal Gemmae 

Alume 

Borax 

Niter 

Dantzick Vitriol 

Oyl of Vitriol 

Rain Water 

Gumm Arabic 

Spirit of Wine well redi 
fied 

Camphire 

Oyl Olive 

Lintfeed Oyl 

Spirit of Turpentine 

Ambar 

A Diamond 



23 to 14 



3851 


to 


3850 


17 


to 


9 


61 


to 


41 


?I 


to 


£0 


25 


to 


16 


5 


to 


3 


17 


to 


II 


35 


to 


24 


22 


to 


M 


^2 


to 


21 


?o? 


to 


200 


10 


to 


7 


529 


to 


396 


l^ 


to 


21 



100 to 73 



3 to 
22 to 
40 to 
25 to 
14 to 
100 to 



2 

15 

27 

17 

9 

41 



The Square of 
BR, to which 
the refra^ing 
force oftheBo. 
dy is propor- 
tionat-e. 



The denfitjCThe refra- 
and fpeci- £tive power 



fc gravity 
bf the Bo- 

4r- 



i'699 

o'ooo52 
2'568 

l'2l3 

i'4025 
i'445 

i'388 

i'i267 

i'i5ii 

i'345 
i'295 

I '041 

o'7845 

i'i79 

o'8765 

I I5II 

i'i948 
i'i626 

l'42 

4^949 



427 

o'ooi2 5 

5'28 

2*252 

2'58 

2^65 

2'72 

2'i43 
i'7i4 
i'7i4 
I '9 
i'7i5 

i'7 
I. 

i'375 

o'866 

©'996 
0^913 
o'932 
o'874 
I '04 

?'4 



of the Body 
in refpeCi 
of its den- 



S979 

4160 
4864 
5386 
543^ 

5450 
6536 

6477 

6570 

6716 
7079 

7551 
6124 

7S45 
8574 

10121 

12551 

12607 
12819 

13222 
13654 

14556 



The refra£tion of the Air in this Table is determined 
by that of the Atmofphere obferved by Aftronomers. 
For if Light pafs through many refracting fubftances or 
mediums gradually denier and denier, and terminated 

L 1 with 



[74] 

with parallel furfaces, the fumm of all the refraftions 
will be equal to the fingle refraStion which it would 
have fufFered in palling immediately out of the firft 
medium ifito the laft. And this holds true, though the 
number of the refrafting fubftances be increafed to infi- 
nity, and the diftances from one another as much de- 
creafed, fo that the Light may be rcfrafted in every 
point of its paffage, and by continual refraftions bent 
into a curve Line. And therefore the whole refradion 
of Light in paffing through the Atmofphere from the 
higheft and rareft part thereof down to the loweft and 
denfeft part, muft be equal to the refraction which it 
would futfer in paffing at like obliquity out of a Va- 
cuum immediately into Air of equal denfity with that 
in the loweft part of the Atmofphere, 

Nov/, by this Table, the refraftions of a Pfeudo-To- 
paz, a Selenitis, Rock Cryftal, liland Cryftal, Vulgar 
Glafs ( that is. Sand melted together ) and Glafs of 
Antimony, which are terreftrial ftony alcalizate con- 
cretes,and Air which probably arifes from fuch fubftances 
by fermentation, though thefebe fubftances very differing 
from one another in denfity, yet they have their refra- 
ctive powers almoft in the fame proportion to one ano- 
ther as their denfities are, excepting that the refraction of 
that ftrange fubftance Illand-Cryftal is a little bigger 
than the reft. And particularly Air, which is 5490 times 
rarer than the Pleudo-Topaz, and 4100 times ra^'er than 
Glafs of Antimony, has notwithftanding its rarity the 
fame refraCtivc power in refpeCl of its denfity which 
thofe two very denfe fubftances have in refpeCt of theirs, 
excepting fo tar as thofe two differ from one another. 

Again, 



Again, the refraftion of Camphire, Oyl-Olive, Lint- 
feed Oyl, Spirit of Turpentine and Amber, which are 
fat fulphureous unftuous Bodies, and a Diamond, which 
probably is an unftuous fubftance coagulated, have their 
refraftive powers in proportion to one another as their 
denfities without any confiderable variation. But the 
refradive power of thefe unftuous fubftances is two 
or three times greater in refpeft of their denfities than 
the refractive powers of the former fubftances in refped 
of theirs. 

Water has a refra<flive power in a middle degree be- 
tween thofe two forts of fubftances, and probably is of 
a middle nature. For out of it grow all vegetable and 
animal fubftances, which confift as well of fulphureous 
fat and inflamable parts, as of earthy lean and alcali- 
zate ones. 

Salts and Vitriols have refradive powers in a middle 
degree between thofe of earthy fubftances and Water, 
and accordingly are compofed of thofe two forts of fub- 
ftances. For by diftillation and rectification of their 
Spirits a great part of them goes into Water, and a great 
part remains behind in the form of a dry fixt earth ca« 
pable of vitrification. 

Spirit of Wine has a refractive power in a middle 
degree between thofe of Water and oyly fubftances, and 
accordingly feems to be compofed of both, united by 
fermentation ; the Water, by means of fome faline Spi- 
rits with which 'tis impregnated, diffolving the Oyl, 
and volatizing it by the aCtion. For Spirit of Wine is 
inflamable by means of its oyly parts, and being diftil- 
led often from Salt of Tartar, grows by every diftilla- 
tion more and more aqueous and flegmatick. And 

LI 2 Chymifts 



Ghymifts obferve, that Vegitables (as Lavender, Rue, 
Marjoram, )^c\) diftilled fer fe , before fermentation 
yield Oyls without any burning Spirits, but after fer- 
mentation yield ardent Spirits without Oyls : Which 
fliews, that their Oyl is by fermentation converted into 
Spirit. They find alfo, that if Oyls be poured in fmall 
quantity upon fermentating Vegetables, they diftil over 
after fermentation in the form of Spirits. 

So then, by the foregoing Table, all Bodies feem to 
have their refraSive powers proportional to their 
denfities, ( or very nearly ; ) excepting fo far as they 
partake more or lefs of fulphurous oyly particles, and 
thereby have their refractive power made greater or 
lefs. Whence it feems rational to attribute the refra- 
ctive power of all Bodies chiefly, if not wholly, to the 
fulphurous parts with which they abound. For it's 
probable that all Bodies abound more or lefs with Sul- 
phurs. And as Light congregated by a Burning-glafs 
a£ts moft upon fulphurous Bodies, to turn them in- 
to fire and flame ; fo, fince all a£tion is mutual. Sul- 
phurs ought to a£t mofl: upon Light. For that the 
action between Light and Bodies is mutual, may appear 
from this Confideration, That the denfefl: Bodies which 
refrad: and reflect Light mofl: ftrongly grow hotteft in 
the Summer-Sun, by the a£tion of the refracted or re- 
flefted Light. 

I have hitherto explained the power of Bodies to re> 
fleft and refra£t, and (hewed, that thin tranfparent 
plates, fibres and particles do, according to their leveral 
thicknefles and denfities, reflect feveral forts of rays, 
and thereby appear of feveral Colours, and by conle- 
quence that nothing more is requifite for producing all 

the. 



[77] 

the Colours of natural Bodies than the ieveral fizes and 
denfities of their tranfparent particles. But whence it 
is that thefe plates, fibres and particles do, according 
to their feveral thicknefles and denfities, refled: fev^eral 
forts of rays, I have not yet explained. To give fome 
infight into this matter, and make way for underflian- 
ding the next Part of this Book, I fliall conclude this- 
Part with a few more Propofitions. Thofe which pre- 
ceded refpedl the nature of Bodies, thefe the nature of 
Light : For both mufl: be underfliood before the reafom 
of their adlions upon one another can be known. And^ 
becaufe the lafl: Propofition depended upon the velo- 
city of Light, 1 will begin with a Propofition of that 
kind. 

PROP. XL 

^' Light is frofagated from luminom Bodies in time^ and 
fiends about [even or eight minutes of an hour in 2^ffi^ig- 
from the Sun to the Earth, 

This was obferved firft by Romer^ and then by others3. 
by means of the Eclipfes of the Satellites oi'^upter,- 
For thefe Eclipfes, when the Earth is between the Sun 
^nAjufiter^ happen about feven or eight minutes fooner 
than they ought to do by the Tables, and when the Earth 
is beyond the Sun they happen about feven or eight mi- 
nutes later than they ought to do; the reafon being, that 
the Light of the Satellites has farther to go in the latter 
cafe than in the former by the Diameter of the Earth's 
Orbit. Some inequalities of time may arife from the 
excentricities of the Orbs of the Satellites ; but thofe 
eannot anfwer in all the Satellites , and at all times 



8] 

to the pofition and diftance of the Earth from the Sun. 
The mean motions of ^ufiter's Satellites is alfo fwifter 
in his defcent from his Aphelium to^ his Perihelium, 
than in his afcent in the other half of his Orb : But this 
inequality has no refped to the pofition of the Earth, 
and in the three interior Satellites is infenfible, as I find 
by computation from the Theory of their gravity. 

PROP. XIL 

iv Every r^y^i>f Light in its fajfage through any refra^ 
Bin^ furface is fut into a certain tranfient conflitution 
or hate , "which in the frogrejs of the ray returns at 
equal intervals^ and dijfojes the ray at every return 
to he eafdy tranjmitted through the next refra(Bing fur^ 
facej and het'ween the returns to be eafdy refiedied by 

it' \{ 

This is manifeft by the 5th, 9th5 i ith and 1 5th Ob- 
fervations. For by thofe Obfervations it appears, that 
, one and the fame fort of rays at equal Angles of inci- 
dence on any thin tranfparent plate, is alternately refle- 
cted and tranfmitted for many fucceflions accordingly, 
as the thicknefs of the plate increafes in arithmetical 
progreffion of the numbers o, 1,1, 3, 4, 5, 6, 7, 8, Iffc, 
fo that if the firft reflexion (that which makes the firfl: 
or innermofl; of the Rings of Colours there defcribed ) 
be made at the thicknefs i,the rays fliallbe tranfmitted at 
the thicknefles o, a, 4, 6, 8, 10, la, Jf^r. and thereby 
make the central Spot and Rings of Light, which ap- 
pear by tranfmiflion, and be reflected at the thicknefs 
I, 3, 5, 7, 9,ai,}5)'^\ and thereby make the Rings which 

appear 



[79 3 

appear by reflexion. And this alternate reflexion and 
tranfmiflion, as 1 gather by the 14th Obiervation, con- 
tinues for above an hundred viciflitudes, and by the 
the Obfervations in the next part of this Book^ for many 
thoufands, being propagated from one furface of a Glafs- 
plate to the other, though the thicknefs of the plate 
be a quarter of an Inch or above : So that this alter- 
nation feems to be propagated from every refracting 
furface to all diftances without end or limitation. 

This alternate reflexion and refradion depends on 
both the furfaces of every thin plate, becaufe it de- 
pends on their diltance. By the aith Obfervation, if 
either furface of a thin plate of Mufcovy-Glafs be wet- 
ted, the Colours caufed by the alternate reflexion 
and refraction grow faint, and therefore it depends on 
them both. 

It is therefore performed at the fecond furface, for 
if it were performed at the firfl:, before the rays ar- 
rive at the fecond, it would not depend on the fe- 
cond « 

It is alfo influenced by fome aftion or difpofition, 
propagated from the firfl: to the fecond, becaufe other- 
wife at the fecond it would not depend on the firfl:. And 
this action or difpofition, in its propagation, intermits 
and returns by equal intervals, becaufe in all its pro- 
grefs it inclines the ray at one diftance from the firfl: 
furface to be reflected by the fecond, at another to be 
tranfmitted by it, and that by equal intervals for innu- 
merable viciflitudes. And becaufe the ray is difpofed 
to reflexion at the diftances i, 3:, 5> 7-, 9>J55'^- and to 
tranfmiflion at the diftances o, a, 4, 6, 8, lo^'^c^ ( for 
its traafmiflion through the firft furface, is at the di- 
ftance 



[8o] 

ftance o, and it is tranfmitted through both toge- 
ther, if their diftance be infinitely Uttle or much lefs 
than I ) the ditpofition to be tranfmitted at the diftances 
1^ 4., 6, 8, 10, ]5fc. is to be accounted a return of the 
fame difpofition which the ray firft had at the diftance o, 
that is at its tranfmiffion through the firft refrafting fur- 
face. AH which is the thing I would prove. 

What kind of aftion or difpofition this is ? Whether 
it confift in ' a circulating or a vibrating motion of the 
ray, or of the medium, or fomething elfe ? I do not 
here enquire. Thpfe that are averfe from affenting to 
any new difcoveries, but fuch as they can explain by an 
Hypothefis, may for the prefent fuppofe, that as Stones 
by falling upon Water put the Water into an undula- 
ting motion, and all Bodies by percuflion excite vibra- 
tions in the Air; fo the rays of Light, by impinging on 
any refrafting or reflecting furface, excite vibrations in 
the refrafting or refleding medium or fubftance, and 
by exciting them agitate the folid parts of the refrafiting 
or refleding Body, and by agitating them caufe the Body 
to grow warm or hot 3 that the vibrations thus excited 
are propagated in the refrafting or reflefting medium 
or fubftance, much after the manner that vibrations are 
propagated in the Air for caufing found, and move 
fafter than the rays fo as to overtake them ; and that 
when any ray is in that part of the vibration which con- 
fpires with its motion, it eafily breaks through a re- 
frading furface, but when it is in the contrary part of 
the vibration which impedes its motion, it is eafily 
reflected ; and, by confequence, that every ray is fuc- 
ceflively difpofed to be eafily reflected, or eafily tranf- 
mitted, by every' vibration which overtakes it. But 

whether 



[8ij 

whether thisHypothefis be true or falfe I do not here 
confider. I content my felf with the bare dilcovery, 
that the rays of Light are by fome caufe or other alter- 
nately difpofed to be refleded or refrafted for many vi- 
ciffitudes. 

"DEFINITION. 

The returns of the diffofition of any ray to be refle^ed 
I zmll call its Fits of eafy reflexion, and thofe of 
its diffofition to be tranfmttted its Fits of eafy tranf- 
miflion, and the fj^ace it fajfes between every re- 
turn and the next return^ the Interval of its 
Fits. 

PROP. XIII. 

' The reafon ^why the fur faces of all thick tranffarent 
Bodies refieB fart of the Light incident on them^ and 
refract the reft^ u^ that fome rays at their incidence are 
in Fits of eafy reflexion^ and others in Fits of eafy tranf^ 
mi£lon, V 

This may be gathered from the i^th Obfervation,- 
where the Light refieSed by thin plates of Air andGIafs, 
which to the naked Eye appeared evenly white all over 
the plate, did through a Prifm appear waved with many 
fucceflions of Light and Darknefs made by alternate fits 
of eafy reflexion and eafy tranfmiflion , the Prifm 
fevering and diftinguifliing the waves of which the 
white refle<3;ed Light was compofed, as was explained 
above. 

M m And 



And hence Light is in fits of eafy reflexion and eafjr 
tranfmiffion, before its incidence on tranfparent Bodies, 
And probably it is put into fuch fits at its firft emiffion 
from luminous Bodies, and continues in them during 
all its progrefs. For thefe fits are of a lafting Nature, 
as will appear by the next part of this Book. 

In this Propofition I fuppofe the tranfparent Bodies 
to be thick, becaufe if the thicknefs of the Body be 
much lefs than the interval of the fits of eafy reflexion 
and tranfmiflion of the rays, the Body lofethits reflecting 
power. For if the rays, which at their entering into 
the Body are put into fits of eafy tranfmiflion, arrive at 
the furthefl: furface of the Body before they be out of 
thofe fits they mufl: be tranfmitted. And this is the 
reafon why Bubbles of Water lofe their reflecting power 
when they grow very thin, and why all opake Bo- 
dies when reduced into very fmall parts become tranf- 
parent. 

PROP. XIV. 

T'hoje Jur faces of tranfparent Bodies^ "which if the ra^ 
h in a fit ofrefradion do refraB it mop f^^ongl^y if the 
f(Vj he in a fit of re^exion do refle3 it mofl eafdp 

For we fliewed above in Prop. 8. that the caufe of 
reflexion is not the impinging of Light on the folid 
impervious parts of Bodies, but fome other power by 
which thofe folid parts aft on Light at a diftance. We 
fliewed alfo in Prop. 9. that Bodies refled and refraft 
Light by one and the fame power varioufly exercifed in 
various circumftances, and in Prop. i. that the mofl: 
ftrongly refrafting furfaces refleft the moft Light : All 

which 



[83] 

which compared together evince and ratify both this 
and the laft Propolition. 

PROP. XV. 

In an^j one and the fame fort of rays emerging in any 
j4ngle out of any refraSing furface into one and the fame 
medium^ the interval of the foUo'wing jits of eafy reflexion 
and tranfmijflon are either accurately or very nearly^ as 
the Redangle of the fecant of the Angle of refra^ion^ and 
^f ^^^ fecant of another jdngle^ "whofe fine is the firft of 
1 06 arithmetical mean froprtionals ^ Set ween the fines 
of incidence and refra^iion counted from the fine of re^ 
frailion, , (^ ij^ 

This is manifeft by the ythpbfervation. 

PRO R XVL 

In fever al forts of rays emerging in equal jingles out 
of any refraSling furface into the fame medium^ the inter^ 
vals of the foUo'uuing fits of eafy reflexion and eafy tranp 
mijfflon are either accurately j or very nearly j as the Cube^ 
roots of the Squares of the lengths of a Chord j which found 
the notes in an Eighty foi, la, fa, fol, la, mi, fa, fol, with 
all their intermediate degrees anfwering to the Colours of 
thofe rays^ according to the Analogy defcribed in the fe^ 
venth Experiment of the fecond Booh 

This is manifeft by the 13 th and i4thObfer¥ations. 

Mm 2 PROP, 



[84] 

PROP. XVII. 

Jfrap of any one fort fafs ferfendicularly into fever al 
mediums^ the intervals of the fits of eafy reflexion and 
tranfmijjlon in any one medium^ ts to thafe intervals in 
any other a^ the fine of incidence to the fine of refraSion^ 
*when the rays fafs out of the firfi of thofe fwo mediums 
into the fecond. 

This is manifeft by the loth Obfervation. 

P R O P. XVIIL 

Jf the rays "which faint the Colour in the confine of 
yellois) and orange fafs ferfendicularly out gf any medium 
into jtir^ the intervals of their fits of eafy reflexion are 
the ^Jih fart of an Inch, u4nd of the fame length are 
the intervals of their fits of eafy tranfmijfion. 

This is manifeft by the 6th Obfervation. 

From thefe Propofitions it is eafy to colle£l: the in- 
tervals of the fits of eafy reflexion' and eafy tranfmif- 
fion of any fort of rays refrafted in any Angle into 
any medium, and thence to know, whether the rays 
fliall be refleded or tranfmltted at their fubfequent 
incidence upon any other pellucid medium. Which 
thing being ufeful for under ftanding, the next part of 
this Book was here to be fet down. And for the fame 
reafoa I add the two following Propol&tions* 

' PROP. 



PROP. XIX. 

• If my fort of rays falling on the polite furface of am 
fellucid medium he refleB>ed hach^ the fits of eafy re^ 
flexion "which they have at the point of reflexion , Jhall 
fiiU continue to return^ and the returns fhall he at di- 
fiances from the point of reflexion in the arithmetical 
progrejfion of the numhers o,^ 4.^ 6, 8, 10, ii^&c. and be- 
tween thefe fits the rays Jhall be in fits of eafy tranf- 
mijfi^on. 

For fince the fits of ealy reflexion and eafy tranf- 
miflion are of a returning nature, there is no reafon 
why thefe fits, which continued till the ray arrived at 
the refleding medium, and there inclined the ray to 
reflexion, fliould there ceafe. And if the ray at the 
point of reflexion was in a fit of eafy reflexion, the 
progrefiion of the difl:ances of thefe fits from that point 
muft begin from o, and fo be of the numbers o, 2,4.5 
6, 8, "^c. And therefore the progrefiion of the di- 
ftances of the intermediate fits of eafy tranfmiflion rec- 
koned from the fame point, mufl: be in the progrefiion 
of the odd numbers i, 5, 5, 7, 9,^'^- contrary to what 
happens when the fits are propagated from points of 
refraftion, 

PROP. XX 

The intervals of the fits of eafy reflexion and eafy 
tranfrrujfon^ propagated fram points of reflexion into any 
medium;^ are equal to the intervals of the like fits -which 
the fame rays would have^ if refradied into the fame 

medium 



[85] 

medium in Angles of jrfra^ion equol to their Angles of 
reflexion . 

For when Light is refleded by the fecond furface of 
thin plates, it goes out afterwards freely at the firft fur- 
face to make the Rings of Colours which appear by 
reflexion, and by the freedom of its egrefs, makes the 
Colours of thefe Rings more vivid and ftrong than thofe 
which appear on the other fide of the plates by the 
tranfmitted Light. The refleded rays are therefore in 
fits of eafy tranfmiffion at their egrefs ; which would 
not always happen, if the intervals of the fits within 
the plate after reflexion were not equal both in length 
and number to their intervals before it. And this confirms 
alio the proportions fet down in the former Propofition. 
For if the rays both in going in and out at the firft furface 
be in fits of eafy tranfmiflion,andthe intervals and num- 
bers of thofe fits between the firft and fecond furface, 
before and after reflexion, be equal | the diftances or 
the fits of eafy tranfmiflion from either furface, muft be 
in the fame progr-eflion after reflexion as before ; that 
is, from the firft furface which tranfmitted them, in 
the progreflion of the even numbers o, 2, 4, 6, S, }5^c. 
and from the fecond which reflected them, in that of 
the odd numbers i^ 3^ 5, 7j ^^* But thefe two Pro- 
pofi.tions will become much more evident by the Obfer^ 
vations in the following part of this Book* 



T H E^ 



] 

THE 

SECOND BOOK 



O F 



OPT 





PARTI 



Oifervations concerning the Reflexions and Colours of 
thick tranf^arent folijhed Vlates, 

THere is no Glafs or Speculum how well foever 
poliflied, but, befides the Light which it refrads 
or refieias regularly , fcatters every way irregularly a 
faint Light, by means of which the polilhed furface, 
when illuminated in a dark Room by a beam of the 
Sun^s Light, may be eafily feen in all pofitions of the 
Eye, There are certain Phgenomena or this fcattered 
Light, which when I firft obferved them, feemed very 
ftrange and furprifing to me. My Obfervations were 
as follows. 



OBS. 



[88] 

O B S. I. 

The Sun fhinlng into my darkened Chamber through 
a Hole I of an Inch wide, I let the intromitted beam 
of Light fall perpendicularly upon a Glafs Speculum 
ground concave on one fide and convex on the other, 
to a Sphere of five Feet and eleven Inches Radius, and 
quick'filvered over on the convex fide. And holding 
a white opake Chart, or a Quire of Paper at the Center 
of the Spheres to which the Speculum was ground, that 
is, at the diftance of about five Feet and eleven Inches 
from the Speculum, in fuch manner, that the beam of 
Light might pafs through a little Hole made in the 
middle of the Chart to the Speculum, and thence be 
refleded back to the fame Hole : I obferved upon the 
Chart foyr or five concentric Irifes or Rings of Colours, 
like Rain-bows, encompaffing the Hole much after the 
manner that thofe, which in the fourth and following 
Obfervations of the fir ft part of this third Book appeared 
between the Objeft-GlaffeSjencompaffed the black Spot, 
but yet larger and fainter than thofe. Thele Rings as 
they grew larger and larger became diluter and fainter, 
ib that the fifth was fcarce vifible. Yet fometimes, 
when the Sun fhone very clear, there appeared faint 
Lineaments of a fixth and feventh. If the diftance of 
the Chart from the Speculum was much greater or much 
lefs than that of fix Feet, the Rings became dilute and 
vanifhed. And if the diftance of the Speculum from 
the Window was much greater than that of fix Feet, 
the reflected beam of Light would be fo broad at the 
diftance of fix Feet from the Speculum where the Rings 

appeared, 



appeared, as to obfcure one^r t^o of the innennoft 
Rmgs.^ And therefore I ufually placed the Speculum 
at about fix Feet from the Window ; fo that its Focus 
might there fall in with the center of its concavity at the 
Rings upon the Chart. And this pofture is always to 
be underftood in the following Oblervations where no 
other is expreft. 

O B S. 11. 

The Colours of thefe Rain-bows fucceeded one anO'- 
ther from the center outwards, in the fame form and 
order with thofe which were made in the ninth Obfer- 
vation of the firft Part of this Book by Light not re- 
fleded, but tranfmitted through the twoObjeft-Glaffes^ 
For, firft, there was in their common center a white 
round Spot of faint Light, fomething broader than the 
reflefted beam of Light ; which beam fometimes fell 
upon the middle of the Spot, and fometimes by a little 
inclination of the Speculum receded from the middle^ 
and left the Spot white to the center. 

This white Spot was immediately encompaffed with 
a dark grey or ruffet, and that darknefs with the Co- 
lours of^e fii'f|^J^j^^which were on the infide next 
the darkne'^little vSSlet and indico, and next to that 
a blue, which on the outfide grew pale, and then fuc- 
ceeded a little greenifh yellow, and after that a brighter 
yellow, and then on the outward edge of the Iris a red 
which on the outfide inclined to purple. 

This Iris was immediately encompaffed With a fe>- 
cond, whofe Colours were in order from the infide 

Nn out- 



[90] 

outwards, purple, blue, green, yellow, light red, a red 
mixed with purple. 

Then immediately followed the Colours of the third 
Iris, which were in order outwards a green inclining 
to purple, a good green, and a red more bright than 
that of the former Iris. 

The fourth and fifth Iris feemed of a bluifh green 
within, and red without, but fo faintly that it was dif- 
ficult to difcern the Colours. 

O B S. IIL 

Meafuring the Diameters of thefe Rings upon the 
Chart as accurately as I could, I found them alfo in 
the fame proportion to one another with the Rings 
made by Light tranfmitted through the two ObjeiS- 
Glaffes. For the Diameters of the four firft of the 
bright Rings meafured between the brighteft parts of 
their orbits, at the diftance of fix Feet from the Specu- 
lum were iJJ, a^^ ijj, jf Inches, whofe fquares are in 
arithmetical progreffion of the numbers i, i, 3, 4. If 
the white circular Spot in the middle be reckoned 
amongft the Rings, and its central Light , where it 
feems to be mofi: luminous, be put equipollent to an 
infinitely little Ring ; the fquares of the Diameters of the 
Rings will be in the progreffion o, i, a, 5, 4, '^c, I 
meafured alfo the Diameters of the dark Circles be- 
tween thefe luminous ones, and found their fquares 
in the progreffion of the numbers \^ i', i{^ ^it^^f-'-^ 
the Diameters of the firft four at the diftance of fix Feet 
from the Speculum, being ij6,2[g,2|j 3f, Inches. If 
the diftance of the Chart from the Speculum was in- 

crealed 



\ 



t90 

creafcd or diminifhed, the Diameters of the Circles were 
iacreafed or diminiihed proportionally. 

O B S. IV. 

By the analogy between thefe Rings and thofe de- 
fcribed in the Obfervations of the fir ft Part of this Book, 
I fufpeded that there were many more of them which 
fpread into one another, and by interfering mixed their 
Colours, and diluted one another fo that they could 
not^^e feen apart. I viewed them therefore through a 
Prifm, as I did thofe in the 24th Obfervation pf the 
firft Part of this Book. And when the Prifm was fo 
placed as by refrading the Light of their mixed Co- 
lours to feparate them, and diftinguiih the Rings from 
one another, as it did thofe in that Obfervation, I could 
then fee them diftinder than before, and eafily num- 
ber eight or nine of them, and fometimes twelve or 
thirteen. And had not their Light been fo very faint^ 
I queftion not but that I might have feen many more, 

. O B S. V. 

Placing a Prifm at the Window to refract the intro- 
mitted beam of Light, and caft the oblong Spe(5lrum 
of Colours on the Speculum : I covered the Speculum 
with a black Paper which had in the middle of it a Hole 
to let any one of the Colours pafs through to the Spe- 
culum, whilft the reft were intercepted by the Paper. 
And now I found Rings of that Colour only which fell 
upon the Speculum. If the Speculum was illuminated 
with red the Rings were totally red with dark inter- 

Nn ^ vals, 



[92] 

vals, if with blue they were totally blue, and lb of the 
other Colours. And when they were illuminated with 
any one Colour, the Squares of their Diameters mea- 
fured between their moft luminous parts, were in the 
arithmetical progreffion of the numbers o, 1,^,9,4, and 
the Squares of the Diameters of their dark intervals in 
the progreffion of the intermediate numbers 7, i{, a{, :^\i 
But if the Colour was varied they varied their magni^ 
tude. In the red they were largeft, in the indico and 
violet leaft, and in the intermediate Colours yellov/, 
green and blue; they were of ieveral intermediate big- 
neffes anfwering to the Colour, that is, greater in yel- 
low than in green^ and greater in green than in blue. 
And hence I knew that when the Speculum was illumi- 
nated with white Light, the red and yellow on the out- 
fide of the Rings were produced by the leaft refrangible 
rays, and the blue and violet by the moft refrangible^ 
and that the Colours of each Ring fpread into the Co- 
lours of the neighbouring Rings on either fide, after 
the manner explained in the firft and fecond Part of this 
Book, and by mixing diluted one another fo that they 
could not be diftinguiflied, unlefs near the center where 
they were leaft mixed. For in this Obfervation I could 
fee the Rings more diftinftly, and to a greater number 
than before, being able in the yellow Light to number 
eight or nine of them, beiides a faint fhadow of a tenth. 
To fatisfy my felf how much the Colours of the feveral 
Rings fpread into one another, I meafured the Diame- 
ters of the fecond and third Rings , and found them 
when made by the confine of the red and orange to be 
the fame Diameters when made by the confine of blue 
md indico;^ as 9 to 85 or thereabouts. For it was hard 

to 



1 



[93] 

to determine this proportion accurately. Alfo the Cir<- 
cles made fucceffively by the red, yellow and green^ 
differed more from one another than thofe made fuccef- 
fiv^ely by the green, blue and indico. For the Circle 
made by the violet was too dark to be feen. To carry 
on the computation, Let us therefore fuppofe that the 
diiferences of the Diameters of the Circles made by the 
outmoft red, the confine of red and orange, the confine 
of orange and yellow, the confine of yellow and green, 
the confine of green and blue, the confine of blue and 
indico, the confine of indico and violet, and outmoft vio- 
let, are in proportion as the diiferences of the lengths 
of a Monochord which found the tones in an Eight ; 
fol^la^fa^fol^la^mi^fa^fol^ that is, as the numbers ^^ 
h, t:? ?z, i, [-J, Is- And if the Diameter of the Circle made 
by the confine of red and orange be 9 A, and that of 
the Circle made by the confine of blue and indico be 
8 A as above, their diiference 9 A — — 8 A will be to 
the difference of the Diameters of the Circles made by 
the outmoft red, and by the confine of red and orange^, 
as f 8 + Ta + ^* + i7 to 9, that is as fr to t or 8 to 5, and to 
the difference of the Circles made by the outmoft violet^ 
and by the confine of blue and indico, as ^s +72 -f t* + 1? 
to i? + ^8, that is, as 17 to h, or as 1 6 to 5. And there- 
fore thefe differences will be i A and U A. Add the 
firft to 9 A and fubdud the laft from 8 A, and you 
will have the Diameters of the Circles made by the 
leaft and moft refrangible rays V A and pf A. Thefe 
Diameters are therefore to one another as 75 to 61^ or 
50, to 41, and their Squares as 1500 to 1681, that is^, 
as 3 to 1 very nearly. Which proportion differs not 
much from the proportion of the Diameters of the 



[94] 

^tl^ircles made by the outmoft red and outmoft violet in 
the 1 5 th Obfervation of the firft part of this Book, 

O B S. VL 

Placing my Eye where thefe Rings appeared plaineflr, 
I faw the Speculum tinged all over with waves of Co- 
lours ( red, yellow, green, blue ; ) like thofe which in 
the Obfervations of the firft Part of this Book appeared 
between the Obje£t-Glafles and upon Bubbles of Water, 
but much larger. And after the manner of thofe, they 
w^ere of various magnitudes in various pofitions of the 
Eye, fwelling and {hrinking as I moved my Eye this 
way and that way. They w^re formed like Arcs of 
xoncentrick Circles as thofe were, and when my Eye 
was over againft the center of the concavity of the Spe- 
culum (that is, 5 Feet and 10 Inches diftance from the 
Speculum) their common center was in a right Line 
with that center of concavity, and with the Hole in the 
Window. But in*other poftures of my Eye their center 
had other pofitions. They appeared by the Light of 
the Clouds propagated to the Speculum through the 
Hole in the Window, and when the Sun fhone through 
that Hole upon the Speculum, his Light upon it was 
of the Colour of the Ring whereon it fell, but by its 
fplendor obfcured the Rings m.ade by the Light of the 
Clouds, unlefs when the Speculum was removed to a 
great diftance from the Window, fo that his Light upon 
it might be broad and faint. By varying the pofition of 
my Eye, and moving it nearer to or farther from the 
direft beam of the Sun's Light, the Colour of the Sun's 
i:efieded Light conftantly varied upon the Speculum, 

as 






as It did upon my Eye, the lame Colour always ap- 
pearing to a By-ftander upon my Eye which to me ap- 
peared upon the Speculum. And thence I knew that 
the Rings of Colours upon the Chart were made by thefe 
reflected Colours propagated thither from the Specu- 
lum In feveral Angles, and that their production de- 
pended not upon the termination of Light and Shad- 
dow. 

O B S. VIL 

By the Analogy of all thefe Phaenomena with thofe of 
the like Rings of Colours defcrlbed In the firft Part of 
this Book, It feemed to me that thefe Colours were 
produced by this thick plate of Glafs, much after the 
manner that thofe were produced by very thia 
plates. For, upon tryal, I found that if the Quick- 
lilver were rubbed off from the back-fide of the Specu- 
lum, the Glafs alone would caufe the fame Rings of 
Colours, but much mor€ faint than before ; and there- 
fore the Phaenomenon depends not upon the Quick- 
filver, unlefs fo far as the Quick-filver by the increafing 
the reflexion of the back- fide of the Glafs increafes the 
Light of the Rln^s of Colours. I found alfo that a Spe- 
culum of metal without Glafs made fome years fince 
for optical ufes, and very well wrought, produced none 
of thofe Rings ; and thence I underftood that thefe 
Rings arlfe not from one fpecular furface alone , but 
depend upon the two furfaces of the plate of Glafs where- 
of the Speculum was made, ancl upon the thicknefs of 
the Glafs between them. For as in the 7th and 19th 
Obfervations of the firft Part of this Book a thin plate 

of 



'©f Air, Water, or Glafs of an even thicknefs appeared 
of one Colour when the rays were perpendicular to it, 
of another when they were a little oblique, of another 
when more oblique, of another when ftill more oblique, 
and fo on ; fo here, in the fixth Obfervation, the Light 
which emerged out of the Glafs in feveral obliquities, 
made the Glafs appear of feveral Colours, and being 
propagated in thofe obliquities to the Chart, there pain- 
ted Rings of thofe Colours. And as the reafon why a 
thin plate appeared of feveral Colours in feveral obli- 
quities of the rays,was,that the rays of one and the fame 
fort are reflected by the thin plate at one obliquity and 
tranfmitted at another, and thofe of other forts tranf- 
mitted where thefe are retledted, and reflefted where 
thefe are tranfmitted : So the reafon why the thick 
plate of Glafs whereof the Speculum was made did ap- 
pear of various Colours in various obliquities, and in 
thofe obliquities propagated thofe Colours to the Chart, 
was, that the rays of one and the fame fort did at one 
obliquity emerge out of the Glafs, at another did not 
emerge but were reflefted back towards the Quick-fil- 
ver by the hither furface of the Glafs, and accordingly 
as the obliquity became greater and greater emerged 
and were retiefted alternately for many fucceffions, and 
that in one and the fame obliquity the rays of one fort 
were refleded, and thofe of another tranfmitted. This 
is manifeft by the firft Obfervation of this Book : For 
in that Obfervation, when the Speculum was illumi- 
nated by any one of the prifmatick Colours, that Light 
made many Rings of the fame Colour upon the Chart 
with dark intervals, and therefore at its emergence out 
of the Speculum was alternately tranfmitted, and not 

tranf- 



97] 

tranfmitted from the Speculum to the Chart for many 
fucceffions^ according to the various obliquities of its 
emergence. And when the Colour caft on the Specu- 
lum by the Prifm was varied, the Rings became o-f 
the Colour caft on it, and varied their bignefs with their 
Colour, and therefore the Light was now alternately 
tranfmitted and not tranfmitted from the Speculum to 
the Lens at other obliquities than before. It feemed to 
me therefore that thefe Rings were of one and the fame 
original with thofe of thin plates, but yet with this 
difference that thofe of thin plates are made by the al- 
ternate reflexions and tranfmiflions of the rays at the 
fecond furface of the plate after one paffage through it : 
But here the rays go twice through the plate before 
they are alternately reflefted and tranfmitted ; firft, 
they go through it from the firft furface to the Quick- 
filver, and then return through it from the Quick-filver 
to the firft furface, and there are either tranfmitted to 
the Chart or refleded back to the Quick-filver, ac- 
cordingly as they are in their fits of eafie reflexion or 
tranfmilnon when they arrive at that furface. For the 
intervals of the fits of the rays which fall perpendicu- 
larly on the Speculum, and are reflected back in the 
fame perpendicular Lines, by reafon of the equality of 
thefe Angles and Lines,are of the fame length and num- 
ber within the Glafs after reflexion as before by the 
19th Propofition of the third Part of this Book. And 
therefore fince all the rays that enter through tlie firft 
furface are in their fits or eafy tranfmiffion at their en* 
trance, and as many of thefe as are refleSed by the fe» 
cond are in their fits of eafy reflexion there, all thefe 
muft be again in their fits of, eafy tranfmiflion at their 

O o return 



«f 



C 98 ] 

return to the firft, and by confequence there go out of 
the Glafs to the Chart, and form upon it the white 
Spot of Light in the center of the Rings. For the rea- 
fon holds good in all forts of rays , and therefore all 
forts muft go out promifcuoully to that Spot, and by 
their mixture cauie it to be white. But the intervals 
of the fits of thofe rays which are reflefted more ob- 
liquely than they enter, muft be greater after reflexion 
than before by the 15 th and 10th Prop. And thence 
it may happen that the rays at their return to the firft 
furface, may in certain obliquities be in fits of eafy re- 
flexion, and return back to the Quick-filver, and in 
other intermediate obliquities be again in fits of eafy 
tranfmiflion, and fo go out to the Chart, and paint on 
it the Rings of Colours about the white Spot. And 
becaufe the intervals of the fits at equal obliquities are 
greater and fewer in the lefs refrangible rays, and lefs 
and more numerous in the more refrangible, therefore 
the leis refrangible at equal obliquities fhall make fewer 
Rings than the more refrangible, and the Rings made 
by thofe fhall be larger than the like number of Rings 
made by thefe ; that is, the red Rings fhall be larger 
than the yellow, the yellow than the green, the green 
than the blue^ and the blue than the violet, as they 
were really found to be in the 5th Obfervation. And 
therefore the firft Ring of all Colours incompafiing the 
white Spot of Light ihall be red without and violet 
within, and yellow, and green, and blue in the middle, 
as it was found in the fecond Obfervation; and thefe 
Colours in the lecond Ring, and thofe that follow ihall 
be more expanded till they fpread into one another,, 
and blend one another by interfering. 

Thefe 



[99 3 

Thefe feem to be the reafons of thefe Rings in ge- 
neral, and this put me upon obferving the thicknefs of 
the Glafs, and confidering whether the dimenfijons and 
proportions of the Rings rnay be. truly derived from it 
by computation. 

O B S. VIIL 

I meafured therefore the thicknefs of this concavo- 
convex plate of Glafs, and found it every- where 4 of an 
Inch precifely. Now, by the 6th Obfervation of the 
firft Part of this Book, a thin plate of Air tranfmits the 
brighteft Light of the firft Ring, that is the bright yel- 
low, when its thicknefs is the ggoooth part of an Inch, 
and by the i oth Obfervation of the fame part, a thin 
plate of Glafs tranfmits the lame Light of the fame Ring 
when its thicknefs is lefs in proportion of the fine of 
refraction to the fine of incidence, that is, when its 
thicknefs is the r^th or ,375^5th part of an Inch, fup- 
pofing the fines areas 11 to 17. And if this thicknefs 
be doubled it tranfmits the fame bright Light of the 
fecond Ring, if tripled it trantmits that of the third, 
and fo on, the bright yellow Light in all thefe cafes be- 
ing in its fits of tranfmiflion. And the-refore if its thick- 
nefs be multiplied ^4586 times fo as to become \ of an 
Inch it tranfmits the fame bright Light of the 34386th 
Ring. Suppofe this be the bright yellow Light tranf- 
mitted perpendicularly from the reflefting convex fide 
of the Glafs through the concave fide to the white Spot 
in the center of the Rings of Colours on the Chart : And 
by a rule in the feventh Obfervation in the firft Part of 
the firft Book, and by the 15th and ^ oth Propofitions 

O o 2 of 



[ lOO ] 

of the third Part of this Book, if the rays be madeob- 
fique to the Glafs, the thicknefs of the Glafsrequi- 
fite to tranfmit the fame bright Light of the fame Ring 
in any obliquity. is to t^is thicj^ne^ of '- of an Inch, as 
the fecant of ast^nsle ^fTSfeMeTs the firft of an hun- 
dred and fix arithmetical means between the fines of 
incidence and refraftion, counted from the fine of inci- 
dence when the refraftion is made out of any plated Bo- 
dy into any medium incompafling it, that is, in this cafe, 
out of Glafs into Air. Now if the thicknefs of the Glafs 
be increafed by degrees,fo as to bear to its firft thicknefs, 
( viz. that of a quarter of an Inch ) the proportions 
which 54-386 (the number of fits of the perpendicular 
rays in going through the Glafs towards the white Spot 
in the center of the Rings,) hath to 34-385, 34384, 
54383 and 3438a (the numbers of thefits of the oblique 
rays in going through the Glafs towards the firft, fe- 
cond, third and fourth Rings of Colours,) and if the 
firfl thicknefs be divided into 1 00000000 equal parts, 
the increafed thicknefles will be 100002908, 100005816, 
100008725 and 100011633^ and the Angles of which thefe 
thickneffes are fecants will be a6' 13", 37' tj",^ 45' 6" and 
5 a' a 6", the Radius being 1 00000000 ; and the fines of 
thefe Angles are 762, 1079,, 1321 and 15^5, and the 
proportional lines ofrefraftion 1172, 1659, 2031 and 
2.34.5, the Radius being 1 00000. For fince the fines 
of incidence out of Glafs into Air are to the fines, 
of refraftion as 11 to 1 7, and to the above-mentioned 
fecants as 11 to the firfl of 106 arithmetical means 
between 11 and 17, that is as 11 to n,^, thofe fe- 
cants will be to the fines of refraction as ii^-^ to 17, 
and by this Analogy will give thefe fines. So then 

if 



[ lOI ] 

if the obliquities of the rays to the concave furtacc of 
the Glafs be luch that the fines of their refradion in 
paffing out of the Glafs through that furface into the. 
Air be 1172, ^^59^ ^031,^ ^i^S-) the bright Light of 
the 34:586th Ring (hall emerge at the thickneffes of the 
Glafs which are to \ of an Inch as 34.386 to 34385^ 
34.384, 34.383, 34.382, refpeftively. And therefore if 
the thicknefs in all thefe cafes be \ of an Inch, (as it is in 
the Glals of which the Speculum was made) the bright 
Light of the 34.385th Ring (hall emerge where tlw. fine, 
ofrefradtionis 1 171, and thatof the.34.384.th,384.383th 
and 34381th Ring where the fine is i659,.^q3J, and 
1345 refpedively. And in thefe Angles of refraction, 
the Light of thefe Rings (hall be propagated from the. 
Speculum to the Chart, and there paint Rings about the 
white central round Spot of Light which we laid was 
the Light of the 34386th Ring. And the Semidiame- 
ters of thefe Rings (hall fubtend the Angles of refraftion 
made at the concave iurface of the Speculum, and by 
confequence their Diameters (hall be to the diftance of 
the Chart from the Speculum as thofe fines of refradion 
doubled are to the Radius that is as 11 7a, 1659, ^03 1^ 
and a 345,. doubled are to looooo. And therefore if. 
the diftance of the. Chart from the concave furface of 
the Speculum be fix Feet (as it was in the third of thefe. 
Obfervations) the Diameters of the Rings of this bright 
yellow Light upon the Chart fhall be i'688, 2^389^,. 
2V5j 3'37 5 Inches : For thefe Diameters are to 6 Feet 
as the above-mentioned fines doubled are to the Radius. 
Now thefe Diameters of the bright yellow Rings, thus 
found by computation are the very fame with thofe 
found in the third of thefe Obfervations by meafuring^ 

them^ 



tl02] 

them, (viz, with ifi' ^^ ^li')and 3'- Inches, and there- 
fore the Theory of deriving thefe Rings from the thick- 
nefs of the plate of Glafs of which the Speculum was 
made, and from the obliquity of the emerging rays agrees 
with the Obfervation. In this computation I have 
equalled the Diameters of the bright Rings made by 
Light of all Colours, to the Diameters of the Rings 
made by the bright yellow. For this yellow makes the 
brighteft part of the Rings of all Colours. If you defire 
the Diameters of the Rings made by the Light of any 
other unmixed Colour, you may find them readily by 
putting them, to the Diameters of the bright yellow ones 
in a fubduplicate proportion of the intervals of the fits 
of the rays of thofe Colours when equally inclined to 
the refrading or refleding furface which caufed thofe 
fits, that is, by putting the Diameters of the Rings made 
by the rays in the extremities and limits of the feven 
Colours, red, orange, yellow, green, blue, indico, violet, 
proportional the Cube-roots of the numbers, i, f , 6 ' 4 5 
Mo ?6> i' which exprefs the lengths of a Monochard 
founding the notes in an Eight : For by this means the 
Diameter of the Rings of thefe Colours will be found 
pretty nearly in the fame proportion to one another, 
which they ought to have by the fifth of thefe Obfer- 
vations. 

And thus I fatisfied my felf that thefe Rings were of 
the fame kind and original with thofe of thin plates, 
and by confequence that the fits or alternate difpofi- 
tions of the rays to be reflefted and tranfmitted are pro- 
pagated to great diftances from every reflefting and re- 
fracting furface. But yet to put the matter out of doubt 
1 added the foUowincr Obfervation. 

O B S. 



C 103 ] 

O B S- IX. 

If thefe Rings thus depend on the thicknefs of the plate 
of Glafs their Diameters at equal di fiances from feveral 
Speculums made of fuch concavo-convex plates of Glafs 
as are ground on tl\e fame Sphere, ought to be recipro- 
cally in a fubduplicate proportion of the thicknefles of 
the plates of Glafs. And if this proportion be found 
true by experience it v^ill amount to a demonftration 
that thefe Rings ( like thofe formed in thin plates ) do 
depend on the thicknefs of the Glafs. I procured there- 
fore another concavo-convex plate of Glafs ground on 
both fides to the fame Sphere with the former plate : 
Its thicknefs was |, parts of an Inch ; and the Diameters 
of the three fir ft bright Rings meafured between the 
brighteft parts of their orbits at the diftance of 6 Feet 
from the Glafs were 3. 4^. 5g. Inches. Now the thick- 
nefs of the other Glafs being \ of an Inch was to thick- 
nefs of this Glafs as^to^j that is as ^i to 10, or 
310000000 to loooooooo^ and the roots of thefe numbers 
are 17607 and loooo, & in the proportion of the firft 
of thefe roots to the fecond are the Diameters of the 
bright Rings made in this Obfervation by the thinner 
Glafs, 5. 4-1. 55 to the Diameters of the fame Rings made 
in the third of thefe Obfervations by the thicker Glafs 
i;^. a2 i;]j that is, the Diam.eters of the Rings are reci- 
procally in a fubduplicate proportion of thickneflfes of 
the plates of Glafs. 

So then in plates of Glafs which are alike concave on 
one fide, and alike convex on the other fide, and alike 
quick-filvered on the convex fides, and differ in nothing 

but 



[io4l 

but their thickueis, the Diameters of the Rings are re- 
ciprocally in a fubduplic ate proportion of the thickneffes 
of the plates. And this iliews lufficiently that the Rings 
'depend on both the furfaces of the Glafs. They de- 
pend on the convex furface becaufe they are more lu- 
minous when that furface is quick-filvered over than 
when it is without Quick-filver. They depend alfo 
upon the concave furface, becaufe without that furface 
a Speculum makes them not. They depend on both 
furfaces and on the diftances between them , becaufe 
their bignefs is varied by varying only that diftance. 
And this dependance is of the fame kind with that 
iwhich the Colours of thin plates have on the diftance 
of the furfaces of thofe plates , becaufe the bignefs 
of the Rings and their proportion to one another, 
and the variation of their bignefs ariling from the varia- 
tion of the thicknefs of the Glafs, and the orders of 
their Colours, is fuch as ought to relult from the Propo- 
litions in the end of the third Part of this Book, derived 
from the the Phaenomena of the Colours of thin plates 
fet down in the firft Part. 

There are yet other Phaenomena of thefe Rings of 
Colours but fuch as follow from the fame Propofitions, 
and therefore confirm both the truth of thofe Propofi- 
tions, and the Analogy between thefe Rings and the 
Rings of Colours made by very thin plates. I fhall 
fubjoyn fome of them. 



O B S. 



O B S. X. 

When the beam of the Sun's Light was refleded back 
from the Speculum not direCtly to the Hole in the Win- 
dow, but to a place a little diftant from it, the common 
center of that Spot, and of all the Rings of Colours fell 
in the middle way between the beam of the incident 
Light, and the beam of the refleded Light, and by 
confequence in the center of the fpherical concavity of 
the Speculujn, whenever the Chart on which the Rings 
of Colours tell was placed at that center. And as the 
beam of relieved Light by inclining the Speculum re- 
ceded more and more from the beam of incident Light 
and from the common center of the coloured Rings be- 
tween them, thole Rings grew bigger and bigger, and 
lb alfo did the white round Spot, and new Rings of Co- 
lours emerged fucceffively out of their common center^ 
and the white Spot became a white Ring encompaffing 
them ; and the incident and reiieded beams of Light 
alw^ays fell upon the oppofite parts of this Ring, illumi- 
nating its perimeter like two mock Suns in the oppofite 
parts of an Iris. So then the Diameter of this Ring, 
meafured from the middle of its Light on one fide to 
the middle of its Liglii: on the other fide, was always 
equal to the diftance between the middle of the incident 
beam of Light, and the middle of the refleded beam 
meafured at the Chart on which the Rings appeared : 
And the rays which formed this Ring were refleSed by 
the Speculum in Angles equal to their Angles of inci- 
dence, and by coniequence to their Angles of refradion 
at their entrance into the Glafs, but yet their Angles of 

P p reflexion 



[10^] 

reflexion were not in the fame planes with their Angles 
of incidence, 

O B S. XL 

The Colours of the new Rings were in a contrary- 
order to thofe of the former, and arofe after this man- 
ner. The white round Spot of Light in the middle of 
the Rings continued white to the center till the diftance 
of the incident and reflected beams at the chart was 
about I parts of an Inch, and then it began to grow 
dark in the middle. And when that difliance was about 
if^of an Inch, the white Spot was become a Ring en- 
compafling a dark round Spot which in the middle in- 
clined to violet and indico. And the luminous Rings 
incompafling it were grown equal to thofe dark ones 
which in the four firfl: Obfervations encompafled them, 
that is to fay, the white Spot was grown a white Ring 
equal to the firfl: of thofe dark Rings, and the firfl: of 
thofe luminous Rings was now grown equal to the fe- 
cond of thofe dark ones, and the fecond of thofe lumi- 
nous ones to the third of thofe dark ones, and fo on. 
For the Diameters of the luminous Rings were now i J3, 
^76 5 ^i? 3h,^^^ Inches. 

When the diftance between the incident and refleded 
beams of Light became a little bigger, there emerged 
out of the middle of the dark Spot after the indico a 
blue, and then out of that blue a pale green, and foon 
after a yellow and red. And when the Colour at the 
center was brighteft, being between yellow and red, 
the bright Rings were grown equal to thofe Rings which 
in the four firfl Obfervations next encompafled them; 

tliat 



[loy] 

that Is to fay^ the white Spot in the middle of thofe 
Rings was now become a white Ring equal to the firft 
of thofe bright Rings, and the firft of thofe bright ones 
was now becomie equal to the fecond of thofe, and fo 
on. For the Diameters of the white Rings, and of the 
other luminous Rings incompaffing it, were now lii ^ 
qI, lii, ^s^lf^c. or thereabouts. 

When the diftance of the two beams of Light at the 
Chart was a little more increafed, there emerged out 
of the middle in order after the red, a purple, a blue, 
a green, a yellow, and a red inclining much to purple, 
and when the Colour was brighteft being between yel- 
low and red, the former indico, blue, green, yellow and 
red, were become an Iris or Ring of Colours equal 
to the firft of thofe luminous Rings which appeared in 
the four firft Obfervations, and the white Ring which 
was now become the fecond of the luminous Rings was 
grown equal to the fecond of thofe, and the firft of 
thofe which was now become the third Ring was be- 
come the third of thofe, and fo on. For their Diame- 
ters were 1^6, ^8, afi, ^f Inches, the diftance of the 
two beams of Light, and the Diameter of the white 
Ring being 2^ Inches. 

When thefe two beams became more diftant there 
emerged out of the middle of the purplifli red, firft a 
darker round Spot, and then out ot the middle of that 
Spot a brighter. And now the former Colours (purple, 
blue, green, yellow, and purplifh red ) were become a 
Ring equal to the firft of the bright Rings mentioned in 
the four firft Obfervations , and the Ring about this 
Ring were grown ^qual to the Rings about that re- 
fpeStively ; the diftance between the two beams of 

P'p a Light 



[io8] ; 

Li^ht and the Diameter of the white Ring ( which 
wa^ now become the third Ring) being about 3 In- 
ches. 

The Colours of the Rings in the middle began rrow 
to grow very dilute^ and if the diftance between the 
two beams was increafed half an Inch, or an Inch m.ore, 
they vanifhed whilft the white Ring, with one or two 
of the Rings next it on either fide, continued ftii! vi- 
fible. But if the diftance of the two beams of Light 
was ftill more increafed thefe alfo vanifhed : For the 
Light which coming from feveral parts of the Hole in 
the Window fell upon the Speculum in feveral Angles of 
incidence made Rings of feveral bigneffes, which diluted 
and blotted out one another, as I knew by intercepting 
fome part of that Light. For if I intercepted that part 
which was neareft to the Axis of the Speculum the 
Rings would be lefs, if the other part which was re> 
moteft from it they would be bigger. 

O B S, XIL 

When the Colours of the Prifm were eaft fucceffively 
on the Speculum, that Ring which in the two laft Ob- 
fervations was white, was of the fame bignefs in all the 
Colours, but the Rings without it were greater in the 
green than in the blue, and ftill greater in the yellow, 
and greateft in the red. And, on the contrary, the 
Rings within that white Circle were lefs in the green 
than in the blue, and ftill lefs in the yellow, and leaft 
in the red. For the Angles of reflexion ofthofe rays 
which made this Ring being equal to their Angles of 
incidence, the fits of every refieded ray within the Glafs 

after 



^ . [109] 

after reflexion are equal in length and nuinber to tlie 
i fits of the fame ray within the Glafs before its incidence 
jt on the refleding furface; and therefore iince all the rays 
of all forts at their entrance into the Glafs were in a fit 
of tranfmiflion, they were alio in a fit of tranfmiffion at 
their returning to the fame furface after reflexion ; and 
by confequence were tranfmitted and went out to the 
white Ring on the Chart. This is the reafon why that 
Ring was of the fame bignefs in all the Colours,, and 
why in a mixture of all it appears white. But in rays 
which are reflefted in other Angles^ the intervals of the 
fits of the leaft refrangible being greatefl:, make the 
Rings of their Colour in their progrefs from this white 
Ring, either outwards or inwards, increafe or decreafe 
by the greateft fleps ; fo that the Rings of this Colour 
without are greateft, and within leaft. And this is the 
reafon why in the laft Obfervation, when the Specu- 
lum was illuminated with white Light, the exterior 
Rings made by all Colours appeared red without and 
blue within, and the interior blue without and red 
within. 

Thefe are the Phaenomena of thick convexo-concave 
plates of Glafs, which are every where of the fame 
thicknefs. There are yet other Phenomena when thefe 
plates are a little thicker on one fide than en the 
other, and others when the plates are more or lefs con- 
cave than convex, or plano-convex,, or double-conveXo 
For in all thefe cafes the plates make Rings of Colours^ 
but after various manners ^ all which, fo far as I have 
yet obferved, follow from the Propolitions in the end 
of the third part of this Book, and fo confpire to con- 
firm the truth of thofe Propofitions. But the Phaeno- 
mena. 



[no] 

niena are too various, and the Calculations whereby 
they follow from thofe Propofitions too intricate to be 
here profecuted. I content my felf with having profe- 
cuted this kind of Phsenomena fo far as to difcover their 
caufe, and by difcovering it to ratify the Propofitions 
in the third Part of this Book. 

O B S. XIII. 

As Liglit reflected by a Lens quick- filvered on the 
back'fide makes the Rings of Colours above de- 
fcribed, fo it ought to make the like Rings of Colours 
in paffing through a drop of Water. At the firft re- 
flexion of the rays within the drop, fome Colours ought 
to be tranfmitted, as in the cafe of a Lens, and others 
to be reflefted back to the Eye. For inftance, if the 
Diameter of a fmall drop or globule of Water be about 
the 5octh part of an Inch, fo that a red-making ray in 
paffing through the middle of this globule has a 50 fits 
of eafy tranfmiffion within the globule, and that all the 
red -making rays whicli are at a certain diftance from 
this middle ray round about it have ^4.9 fits within the 
globule, and all the like rays at a certain further di- 
ftance round about it have 148 fits, and all thofe at a 
certain further diftance 24.7 fits, and fo on ; thefe con- 
centrick Circles of rays after their tranfmiffion, falling 
on a white Paper, will make concentrick rings of red 
upon the Paper , fuppofing the Light which paffes 
through one imgle globule ftrong enough to be fenfible. 
And, in like manner, the rays of other Colours will 
make Rings of other Colours. Suppofe now that in a 
fair day the Sun lliines through a thin Cloud of fuch 

globules 



^\}l 1 1 ] 

globules of Water or Hail^ and that the globules are all 
of the fame bignefs,and the Sun feen through this Cloud 
(hall appear incompafled with the hke concentrick Rings 
of Colours, and the Diameter of the firft Ring of red 
(hall be 7; degrees, that of the fecond i O; degrees, that 
of the third 12 degrees 33 minutes. And accordingly 
as the globules of Water are bigger or lefs, the Rings 
fhall be lefs or bigger. This is the Theory, and expe- 
rience anfwers it. For in June 1691. I faw by reflexion 
in a Veflel of ftagnating Watier tliree Halos Crowns or 
Rings of Colours about the Sun, like three little Rain- 
bows, concentrick to his Body. The Colours of the 
firft or innermoft Crown were blue next the Sun, red 
without, and white in the middle between the blue 
and red. Thofe of the fecond Crown were purple and 
blue within, and pale red without, and green in the 
middle. And thofe of the third were pale blue with- 
in, and pale red without; theie Crowns inclofed one 
another immediately, fo that their Colours proceeded 
in this continual order from the Sun outward : blue, 
white, red ; purple, blue, green, pale yellow and red ; 
pale blue, pale red. The Diameter of the fecond Crown 
meafured from the middle of the yellow and red on one 
fide of the Sun, to the middle of the fame Colour on 
the other fide was 9^ degrees, or thereabouts. The Dia- 
meters of the firft and third I had not time to meafure, 
but that of the firft feemed to be about five or fix de- 
grees, and that of the third about twelve. The like 
Crowns appear fometimes about the Moon 3 for in the 
beginning of the year 1 664, Feh\ 1 9th at night, I faw 
two fuch Crowns about her. The Diameter of the firft 
or innermoft was about three degrees, and that of the 



[II2] 

lecond about five degrees and an half. Next about the 
Moon was a Circle of white, and next about that the 
inner Crown which was of a bluiih green within next the 
white, and of a yellow and red without, and next about 
thefe Colours were blue and green on the infide of the 
outward Crown, and red on the outfide of it. At the 
fame time there appeared a Halo about 12 degre-:^^ 35' 
diftant from the center of the Moon. It was Elliptical, 
and its long Diameter was perpendicular to the Horizon 
verging below fartheft from the Moon. I am told thatS 
the Moon has fometimes three or more concentrick 
Crowns of Colours incompaffing one another next about 
her Body. The more equal the globules of Water or 
Ice are to one another, the more Crowns of Colours 
will appear, and the Colours will be the more lively. 
The Halo ar the diftance of cli'- degrees from the Moon 
is of another fort. By its being oval and remoter from 
the Moon below than above, I conclude, that it v/as 
made by refraftion in fome fort of Hail or Snow floaling 
in the Air in an horizontal Pofture, the refrafting Angle 
being about 58 or 60 degrees. 



T H 



J 



["3] 

THE 

THIRD BOOK 

O F 



O P T I C K 




Oifervations concerning the Inflexions of the rays of Light j 
and the Colours made thereby. 

GRimaldo has informed us, that if a beam of the 
Sun's Light be let into a dark Room through a 
very fmall Hole, the fliadows of things in this Light 
will be larger than they ought to be if the rays went 
on by the Bodies in ftreight Lines, and that thefe fha- 
dows have three parallel fringes, bands or ranks of co- 
loured Light adjacent to them. But if the Hole be 
enlarged the fringes grow broad and run into one ano- 
ther, fo that they cannot be dirtinguiflied. Thefe broad 
fhadows and fringes have been reckoned by fome to pro- 
ceed from the ordinary refraftion of the Air, but with- 
out due examination of the matter. For the circum« 
ftances of the Phaenomenon, fo far as I have obferved 
them, are as follows. 

Qq OBS. 



["4] 

O B S. L 

I made in a piece of Lead a fmall Hole with a Pin, 
whofe breadth wis ihe^ath part of an Incli. For 21 
of thofePins laid together took up the breadth of half 
an Inch. Through this Hole I let into my darkened 
Chamber a beam of the Sun's Light, and found that the 
ihadows of Hairs^Thred^Pins^Straws, and fuch like llen- 
der fubftances placed in this beam of Light, were confider- 
ably broader than they ought to be, if the rays of Light 
pafled on by thefe Bodies in right Lines. And particu- 
larly a Hair of a Man's Head, whofe breadth was but 
the 280th part of an Inch, being held in this Light, at 
the diftance of about twelve Feet from the Hole, did 
caft a ftiadow which at the diftance of four Inches from 
the Hair was the fixtieth part of an Inch broad, that is, 
above four times broader than the Hair, and at the di- 
ftance of tw^o Feet from the Hair was about the eight 
and twentieth part of an Inch broad, that is, ten times 
broader than the Hair, and at the diftance often Feet 
was the eighth part of an Inch broad, that is 35 times 
broader. 

Nor is it material W'hether the Hair be incompaffed 
with Air, or with any other pellucid fubftance. For I 
wetted a poliftied plate of Glafs, and laid the Hair in 
the Water upon the Glafs, and then laying another po- 
liftied plate of. Glafs upon it, fo that the Water might 
fill up the fpace between the Giafles, I held tljiem in 
the aforeiaid beam of Light, fo that the Lighl:4night 
pafs through them perpendicularly, and the ftiadow 
of the Hair was at the iame diftances as big as before. 

The 



[115] 

The fhadows of fcratches made in polifhed plates of 
Glafs were alio much broader than they ought to be, 
and the Veins in polifhed plates of Glafs did alio caft the 
like broad (liadovvs. And therefore the great breadth 
of thefe ihadows proceeds from fome other caufe than 
the refradion of the Air. 

Let the Circle X reprefent the middle of the Hair ; Fig, i 
ADG, BEH, CFI, three rays paffing by one fide of 
the Hair at feveral diftances ; KNQ, LOR^ MPS, 
three other rays pafling by the other fide of the Hair at 
the like diftances; D, E, F and N, O, P, the places 
where the rays are bent in their pafTage by the Hair ; 
G, H, I and Q, R, S, the places where the rays fail on 
a Paper G Q j I S the breadth of the fhadow of the Hair 
caft on the Paper, and T I, V S, two rays paffing to the 
points I and S without bending when the Hair is taken 
away. And it's manifeft that all the Light between 
thefe two rays A I and V S is bent in paffing by the 
Hair, and turned afide from the fhadow IS, becauie if 
any part of this Light were not bent it would fall on 
the Paper within the fhadow, and there illuminate the 
Paper contrary to experience. And becaufe when the 
Paper is at a great diiliance from the Hair, the fhadow 
is broad, and therefore the rays TI and VS are at a 
great diitance from one another, it follows that the 
Hair ads upon the rays of Light at a good diftance in 
their paffing by it. But the a£i:ion is ftrongeil on the 
rays which paf^ by at leaft difl:ances, and grows weaker 
and weaker accordingly as the rays pafs ' by at diftances 
greater and greater, as is reprefented in the Scheme : 
For thence it comes to pais, that the fhadow of the 
Hair is much broader in proportion to the diflance of 

(Iq 2 the 



the Paper from the Hair, when the Paper is nearer the 
Hair than when it is at a great diftance from it, 

O B S. IL 

The flhadows of all Bodies ( Metals, Stones, Glafs^ 
Wood, Horn, Ice, tor. ) in this Light were bordered 
with three parallel fringes or bands of coloured Light, 
whereof that which was contiguous to the Ihadow was 
broadeft and moft luminous, and that which was re- 
moteft from it was narroweft, and fo faint, as not eafily 
to be vifible. It was difficult to diftinguifh the Colours 
unlefs when the Light fell very obliquely upon a fmooth 
Paper, or fome other fmooth white Body, io as to. make 
them appear much broader than they would otherwife 
do. And then the Colours were plainly vifible in this 
order : The firft or innermoft fringe was violet and deep 
blue next the fhadavv, and then light blue, green and 
yellow in the middle, and red without. The fecond 
fringe was almoft contiguous to the firft, and the third 
to the fecond, and both were blue within and yellow 
and red without, but their Colours were very faint 
efpecially thofe of the third. The Colours therefore 
proceeded in this order from the fhadow, violet, indico, 
pale blue, green, yellow, red ; blue, yellow, red ; pale 
blue, pale yellow and red. The Ihadows made by 
fcratches and bubbles in polifhed plates of Glafs were 
bordered with the like fringes of coloured Light. And 
if plates of Looking-glafs floop'd off near the edges with 
a Diamond cut, be held in the fame beam of Light, the 
Light which pafles through the parallel planes of the 
Glafs will be be bordered with the like fringes of Cor 

lours 



["7] 

lours where thofe Planes meet with the Diamond cut, 
and by this means there will fometimes aj3pear four or 
five fringes of Colours. Let AB, CD reprefent theKi>, 2 
parallel planes of a Looking-glafs^ and BD the plane 
of the Diamond-cut, making at B a very obtufe An^le 
with the plane A B. And let all the Light between die 
rays EN I and FBM piafs diredly through the parallel 
planes of the Glafs, and fall upon the Paper between I 
andM, and all the Light between the rays GO and 
HD be refrafted by the oblique plane of the Diamond 
cut B D,and fall upon the Paper between K and L ; and 
the Light which pafles diredly through the parallel 
planes of the Glafs, and falls upon the Paper between. 
I and M, will be bordered with three or more fringes, 
at M. 

O B S. III. 

When the Hair was twelve Feet diftant from the 
Hole, and its fliadow fell pbliq^uely upon a flat white 
fcale of Inches and parts of an Inch placed half a Foot - 
beyond it, and alfo when the fliadow fell perpendicu- 
larly upon the fame fcale placed nine Feet beyond it; 
I meafured the breadth of the fliadow and fringes as 
accurately as I could, and found them in parts of art- 
Inch as follows. 



The 



[ii8] 



The breadth of the Shadow 



The breadth between the middles of the 
brighteft Light of the innermoft fringes 
;-.U^ on either fide the (hadow 



The breadth between the middles of the 
brishteft Light of the middlemoft frin- 
g;es on either fide the fhadow 



The breadth between the middles of the 
brighteft Light of the outmoft fringes 
y&Q) on either fide the fhadow 



The diftance between the middles of the 
brighteft Light of the firft and fecond 
fringes 

The diftance between the middles of the 
brighteft Light of the fecond and third 
fringes 



The breadth of the luminous part (green, 
white, yellow and red ) of the firft 



fringe 



The breadth of the darker fpace between 
the firft and fecond fringes. 

The breaddi of the luminous part of the 
fecond fringe 



The breadth of the darker fpace between 
the fecond and third fringes. 



half O' 


nine 


Foot, 


Feet, 


I 


I 


'i'i 


9 


;»or;, 


7_ 
SO 


• 

I 


4 


23i 


17 


^ «^ T8i 


to 


r 


I 






lio 


. 2X 


■ T 


I 


J 70 


31 

~ J 




r 


r 


173 


32 




[up] 

Thefe meafures I took by letting the fhadow of the 
Hair at half a Foot diftance fall lb obliquely on the 
fcale as to appear twelve times broader than when it 
fell perpendicularly on it at the fame diftance, and fht- 
ring down in this Table the twelfth part of the mea- 
fures I then took. 

O B S. IV, 

When the ftiadovv and fringes were caft obliquely 
upon a fmooth white Body, and that Body was remo- 
ved further and further from the Hair, the firft fringe 
began to appear and look brighter than the reft of the 
Light at the diftance of lefs than a quarter of an Inch 
from the Hair, and the dark line or fhadow between 
that and the fecond fringe began to appear at a lefs di- 
ftance from the Hair than that of the third part of an 
Inch. The fecond fringe began to appear at a diftance 
from the Hair of lefs than half an Inch, and the fliadow 
between that and the third fringe at a diftance lefs than, 
an Inch, and the third fringe at a diftance lefs than three 
Inches. At greater diftances they became much more 
fenfible, but kept very nearly the fame proportion o£ 
their breadths and intervals which they had at their firft 
appearing. For the diftance between the middle of the 
firft and middle of the fecond fringe, was to the diftance 
between the middle of the fecond and middle of the 
third fringe, as three to two, or ten to feven. And 
the laft of thefe two diftances was equal to the breadth 
of the bright Light or luminous part of the firft fringe« 
And this breadth was to the breadth of the bright Light 
of the fecond fringe as feven to four, and to the dark 

mtervai: 



interval of the firft and fecond fringe as three to two, 
and to the hke dark interval between the lecond and 
third as two to one. For the breadths of the fringes 
feemed to be in the progreffion of the numbers i, / 



rX: 



iO 



V \ and their intervals to be in the fame progreffion 
with them ; that is, the fringes and their intervals to- 
gether to be in the continual progreffion of the numbers 
I , /^ -S /\-, /^ J- , l^]^ or thereabouts. And thefe pro- 
portions held the fame very nearly at all diftances from 
the Hair 3 the dark Intervals of the fringes being as 
broad in proportion to the fringes at their firft appea- 
rance as afterwards at great diftances from the Hair, 
though not fo dark and diftinft. 

O B S. V. 

The Sun ffiining into my darkened Chamber through 
a Hole a quarter of an Inch broad ; I placed at the di^ 
ftance of tw^o or three Feet from the Hole a Sheet of 
Paft-board, which was black'd all over on both fides, 
and in the middle of it had a Hole about three quarters 
of an Inch fquare for the Light to pafs through. And 
behind the Hole I faftened tothePaft-board with Pitch 
the blade of a fharp Knife, to intercept fome part of 
the Light which paffed through the Hole. The planes 
of the Paft'board and blade of the Knife were parallel 
to one another, and perpendicular to the rays. And 
vvlien they were fo placed that none of the Sun's Light 
fell on the Paft-board, but all of it paffed through the 
Hole to the Knife, and there part of it fell upon the 
blade of the Knife, and part of it- paffed by its edge : 
I let this part of the Light which paffed by, fall on a 

white 



[ 121 ] 

white Paper two or three Feet beyond the Knife, and 
there faw two ftreams of faint Light (hoot out both 
ways from the beam of Light into the fhadow Hke the 
tails of Comets. But becaufe the Sun's direct Light by 
its brightnefs upon the Paper obfcured thefe faint 
ftreams, fo that I could fcarce fee them, I made a little 
Hole in the midft of the Paper for that Light to pafs 
through and fall on a black cloth behind it ; and then 
I Hiw the two ftreams plainly. They were like one 
another, and pretty nearly equal In length and breadth, 
and quantity of Light. Their Light at that end next 
the Sun's dire£t Light was pretty ftrong for the fpace of 
about a quarter of an Inch, or half an Inch, and in all 
its progrefs from that dire£t Light decreafed gradually 
till it became infenfible. The whole length of either of 
thefe ftreams meafured upon the Paper at the diftance 
of three Feet from the Knife was about fix or eight 
Inches ; fo that it fubtended an Angle at the edge of 
the Knife of about lo or 12, or at moft 14 degrees. 
Yet fometimes I thought I faw it ftioot three or four 
degrees further, but with a Light fo very faint that I 
could fcarce perceive it, and fufpeded it might ( in 
fome meafure at leaft) arife from fome other caufe than 
the two ftreams did. For placing my Eye in that Light 
beyond the end of that ftream which was behind the 
Knife, and looking towards the Knife, I could fee a 
line of Light upon its edge, and that not only when 
my Eye was in the line of the ftreams, but alfo when 
it was without that line either towards the point of the 
Knife, or towards the handle. This line of Light ap- 
peared contiguous to the edge of the Knife, and was 
narrower than the Light of the innermoft fringe, and 

R r narroweft 



[122] 

mrro,weft when my Eye was furtheft from the dlrefl; 
Light, and therefore feemed to pafs between the Light 
of that fringe and the edge of the Knife , and that 
which palled neareft the edge to be moft bent, though 
not all of it. 

O B S. VI. 

I placed another Knife by this fo that their edges 
might he parallel and look towards one another, and 
that the beam of Light might fall upon both the Knives^ 
and fome part of it pafs betw^een their edges. And 
when the diftance of their edges was about the 400th 
part of an Inch tlie ftream parted in the middle, and 
left a fhadow between the two parts. This ihadow 
was fo black and dark that all the Light which paffed 
between the Knives feemed to be bent, and turned afide 
to the one hand or to the other. And as the Knives ftill 
approached one another the fhadow grew broader, and 
the ftreams fhorter at their inward ends which were 
next the fhadow, until upon the contad of the Knives 
the whole Light vanifhed leaving its place to the 
fhadow. 

And hence I gather that the Light which is leaft 
bent, and goes to the inward ends of the ftreams, paf- 
fesby the edges of the Knives at the greateft diftance, 
and this diftance when the ftiadow begins to appear be- 
tween the ftreams is about the eight- hundredth part of 
an Inch. And the Light which pafles by the edges of 
the Knives at diftances ftill lefs and lels is more and 
more bent, and goes to thofe parts of the ftreams w^hich 
are further and further from the, direct Light, becaufc 

when 



[ t23 ] 

when the Knives approach one another till they toiich^ 
thofe parts of the ftreams vaniftl laft which ^re furtheft 
from the dired Light. 

O B S. VIL 

In the fifth Obfervatioh the fringes did riot Appear, 
but by reafon of the breadth of the Hole in the Win- 
dow became fo broad as to run into one another, and 
by joyning make one continued Light in the beginning 
of the ftreams. But in the fixth^ as the Knives ap- 
proached one another, a little before the fhadow ap- 
peared between the two ftreams, the fringes began to' 
appear on the inner ends of the ftreams on either fide 
of the direct Light, three on one fide made by the edge 
of one Knife, and three on the other fide made by the 
edge of the other Knife. They were diftindeft when 
the Knives were placed at the greateft diftance from the 
Hole in the Window, and ftill became more diftind by 
making the Hole lefs, infomuch that I could fometiriies 
fee a faint lineament of a fourth fringe beydnd the three 
above-mentioned. And as the Knives continually ap- 
proached one another, the fringes grew diftinder and 
larger until they vaniftied. The outmoft fringe va- 
niftied firft, and the middlemoft next, and the inner- 
moft laft. And after they were all vanifhed, and tJie 
line of Light which was in the middle between them 
was grown very broad, enlarging it felf on both fides 
into the ftreams of Light defcribed in the fifth Obfer- 
vation, the above-mentioned fliadow began to appear 
in the middle of this line, and divide it along the middle 
mto two lines of Light, and increafed until the whole 

R r 2 Lisht 



[124] 

Light vanifhed. This inlargement of the fringes was 
fo great that the rays which go to the innermoft fringe 
feemed to be bent above twenty times more when this 
fringe was ready to vanifh^ than when one of the Knives 
was taken away. 

And from this and the former Obfervation compared, 
I gather, that the Light of the firft fringe paffed by the 
edge of the Knife at a diftance greater than the eight- 
hundredth part of an Inch, and the Light of the fecond 
fringe paffed by the edge of the Knife at a greater di- 
ftance than the Light of the firft fringe did, and that 
of the third at a greater diftance than that of the fe- 
cond, and that of the ftreams of Light defcribed in 
the fifth and fixth Obfervations paffed by the edges 
of the Knives at lefs diftances than that of any of the 



fringes. 



O B S. VIII. 



I caufed the edges of two Knives to be ground truly 
ftreight, and pricking their points into a board fo that 
their edges might look towards one another, and meet- 
ing near their points contain a reftihnear Angle, I faft- 
ned their handles together with Pitch to make this. 
Angle invariable. The diftance of the edges of the 
Knives from one another at the diftance of four Inches 
from the angular point, where the edges of the Knives 
met, was the eighth part of an Inch, and therefore the 
Angle contained by the edges was about i degr, 54,'. 
The Knives thus fixed together I placed in a beam of 
the Sun's Light, let into my darkened Chamber through 
a Hole the ^ith part of an Inch wide, at the diftance. 

of 



[125] 
of ten or fifteen F^et from the Hole, and let the Light 
which paffed between their edges fell very obliquely 
upon a fmooth white Ruler at the diftance of half an 
Inch, or an Inch from the Knives, and there faw the 
fringes made by the two edges of the Knives run along 
the edges of the fhadows of the Knives in lines parallel 
to thofe edges without growing fenfibly broader, till 
they met in Angles equal to the Angle contained by the 
edges of the Knives, and where they met and joyned 
they ended without croffing one another. But if the 
Ruler was held at a much greater diftance from the 
Paper, the fringes became fomething broader and broader 
as they approached one another, and after they met 
they crofled one another, and then became much broader 
than before. 

Whence I gather that the diftances at which the 
fringes pafs by the Knives are not increafed nor altered 
by the approach of the Knives^ but the Angles in which 
the rays are there bent are much increafed by that ap- 
proach ; and that the Knife which is neareft any ray 
determines which way the ray fliall be bent, and the 
other Knife increafes the bent. 

O B S. IX. 

When the rays fell very obliquely upon the Ruler at 
the diftance of the third part of an Inch from the Knives.^, 
the dark line between the firft and fecond fringe of the 
fliadow of one Knife, and the dark line between the: 
firft and fecond fringe of the ftiadow of the other Knife 
met with one another, at the diftance of the fifth part 
of an Inch from the end of the Light which paffed be- 



tween the Knives at the concourfe of their edges. And 
therefore the diftance of the edges of the Knives at the 
meeting of thefe dark lines was the i6oth part of an 
Inch. For as four Inches to the eighth part of an Inch, 
fo is any length of the edges of the Knives rneafured 
from the point of their concourfe to the diftance of the 
edges of the Knives at the end of that length, and fo is 
the fifth part of an Inch to the 1 6oth part. So then the 
dark lines above-mentioned meet in the middle of the 
Light which pafles between the Knives where they are 
diftant the 1 6oth part of an Inch, and the one half of 
that Light pafles by the edge of one Knife at a diftance 
not greater than the 3aoth part of an Inch, and falling 
upon the Paper makes the fringes of the lliadow of that 
Knife, and the other half paffes by the edge of the 
other Knife, at a diftance not greater than the 320th 
part of an Inch, and falling upon the Paper makes the 
fringes of the (hadow of the other Knife. But if the 
Paper be held at a diftance from the Knives greater than 
the third part of an Inch, the dark lines above-men- 
tioned meet at a greater diftance than the fifth part of 
an Inch from the end of the Light which pafled be- 
tween the Knives at the concourfe of their edges; and 
therefore the Light which falls upon the Paper where 
thofe dark lines meet pafles between the Knives 
where their edges are diftant above the 1 6cth part of 
an Inch. 

For at another time when the two Knives were di-^ 
ftant eight Feet and five Inches from the little Hole in 
the Window, made with a fmall Pin as above, the Light 
which fell upon the Paper where the aforefaid dark 
lines met. pafled between the Knives, where the di- 
ftance 



[127] 

ftance between their edges was as in the following 
Table, when the diftance of the Paper from the Knivel 
was alfo as follows. 



Dijiances of the Paper 
from the Kjiives in 
Inches, 



Difimces between the edges 
of the Kj^ives in milU" 
fimal parts of an Inch. 



li- 


0'0I2. 


3i- 


0'020. 


8;- 


o'o34. 


3^- 


o'o57. . 


96. 


o'oSi. 

i 


151. 


o'oS?. 1 



And hence I gather that the Light which makes the 
fringes upon the Paper is not the fame Light at all di- 
ftances of the Paper from the Knives, but when the Pa» 
per is held near the Knives, the fringes are made by 
Light which paffes by the edges of the Knives at a lels 
diftance, and is more bent than when the Paper is held 
at a greater diftance from the Knives, 

O B S. X. 



When the fringes of the fiiadows of the Knives fell 
perpendicularly upon a Paper at a great diftance from 
the Knives, they w^ere in the form of Hyperbolas, and 
their dimenfions were as follows. Let C A, CB repre^ 
fent lines drawn upon the Paper parallel to the edges of 
the Knives, and between which all the Light would 
fall, if it paffed between the edges of the Knives with- 
out iniiexion; DE a right line drawn through C making 

the 



[128] 

th e Angles A C D, B C E, equal to one another, and 
terminating all the Light whith falls upon the Paper from 
the point where the edges of the Knives meet j eis, fk t, 
and glv, three hyperbolical lines reprefenting the ter- 
minus of the fhadow of one of the Knives, the dark line 
between the firft and fecond fringes of that fhadow, and 
the dark line between the fecond and third fringes of 
the fame fhadow ; x i p, y k q and z 1 r, three other Hy- 
perbolical lines reprefenting the terminus of the fhadow 
of the other Knife, the dark line between the firft and 
fecond fringes of that fhadow, and the dark line be- 
tween the fecond and third fringes of the fame fhadow. 
And conceive that thefe three Hyperbolas are like and 
equal to the former three, and crofs them in the points 
i, k and 1, and that the fhadows of the Knives are termi- 
nated and diftinguifhed from the firft luminous fringes 
by the lines e is and xip, until the meeting andcrof- 
iing of the fringes, and then thofe lines crofs the fringes 
in the form of dark lines, terminating the firft luminous 
fringes within fide, and diftinguiftiing them from ano- 
ther Light which begins to appear at i, and illuminates 
all the triangular fpace ipDEs comprehended by thefe 
dark lines, and the right line DE. Of thefe Hy- 
perbolas one Afymptote is the line DE, and their other 
Afymptotes are parallel to the lines CA and CB. Let 
rv reprefent a line drawn any where upon the Paper 
parallel to the Afymptote D E, and let this line crofs 
the right lines A C in m and B C in n, and the fix dark 
hyperbolical lines in p, q, r ; s, t, v ; and by meafuring 
the diftances ps, qt, rv, and thence cofledting the 
the lengths of the ordinatesnp, nq, nr or ms, mt, 
mv, and doing this at feveral diftances of the line rv^ 

irom 



from the Afymptote DE you may find as many points 
of thefe Hyperbolas as you pleafe, and thereby know 
that thefe curve lines are Hyperbolas diifering little from 
the conical Hyperbola. And by meafuring the lines 
C i , C k , CI, you may find other points of thefe 
Curves. 

For inftance, when the Knives were diftant from the 
Hole in the Window ten Feet, and the Paper from the 
Knives 9 Feet, and the Angle contained by the edges of 
the Knives to which the Angle ACB is equal, was fub- 
tended by a chord which was to the Radius as i to 3 1, 
and the diftance of the line r v from the Afymptote DE 
was half an Inch: I meafured the lines ps, qt, rv, 
and found them o'^ 5, 0*65, o'^S Inches refpedively, 
and by adding to their halfs the line i mn (which here 
was the 1:28th part of an Inch, or o'ooyS Inches ) the 
funis np, nq, nr, were o'i8i8, o'^^iS, o\(^j^ In- 
ches. 1 meafured alfo the diftances of the brighteft 
parts of the fringes which run between pqand st, qr 
and tv, and next beyond r and v, and found them o'*'^^ 
o'S, and I'ly Inches. 

O B S. XL 

The Sun Ihining into my daAened Room through a 
fmall round Hole made in a plate of Lead with a llender 
Pin as above ; I placed at the Hole a Prifm to refrad 
the Light, and form on the oppofite Wall theSpeftrum 
of Colours, defcribed in the third Experiment of the 
firft Book. And then I found that the (badows of all 
Bodies held in the coloured Light between the Prifm 
and the Wall, were bordered with fringes of the Colour 

S s of 



[130] 

of that Light in which they were held. In the full red 
Light they were totally red without any fenfible blue 
or violet^ and in the deep blue Light they were totally 
blue without any fenfible red or yellow ; and fo in the 
green Light they were totally green, excepting a little 
yellow and blue, which were mixed in the green Light 
of the Prifin. And comparing the fringes made in the 
leveral coloured Lights, 1 found that thole made in the 
red Light were largeft, thofe made in the violet were 
leaft, and thofe made in the green were of a middle 
bignefs. For the fringes with which the Ihadow of a 
Man's Hair were bordered, being meafured crofs the 
fhadow at the diftance of fix Inches from the Hair ; the 
diftance between the middle and moll: luminous part of 
the firft or innermoft fringe on one fide of the fhadow^, 
and that of the like fringe on the other fide of the Iha- 
dow, was in the full red Light /^^ of an Inch, and in 
the full violet ^. And the like diftance between the 
middle and moil: luminous parts of the fecond fringes on 
either fide the (hadow was in the full red Light {^ , and 
in the violet '- of an Inch. And thefe diftances of the 
fringes held the fame proportion at all diftances from 
the Hair without any fenfible variation. 

So then the rays which made thefe fringes in the red 
Light paffed by the Hair at a greater diftance than thofe 
did which made the like fringes irl the violet ; and there- 
fore the Hair in caufing thefe fringes adted alike upon, 
the red Light or leaft refrangible rays at a greater di- 
ftance, and upon the violet or moft refrangible rays at 
a lefs diftance, and by thofe adions difpofed the red 
Light into larger fringes, and the violet into fmaller, 
-md the Lights of interm.ediate Colours into fringes of 

inter- 



[I3IJ 

intermediate bigneffes without changing the Colour of 
of any fort of Light* 

When therefore the Hair in tiie firft and fecond of 
thele Obfervations was held in the white beam of the 
Sun's Light, and cafi: a fhadow which was bordered with 
three fringes of coloured Light, thofe Colours arofe not 
from any new modifications impreft upon the rays of 
Light by the Hair, but only from the various intiedlions 
whereby the feveral forts of rays were feparated from 
one another, wliich before reparation by the mixture 
of all their Colours, compofed the white beam of the 
Sun's Light, but whenever fepajated compofe Lights 
of the feveral Colours which they are originally dii'po- 
fed to exhibit. In this 15th Obfervation, where the 
Colours are feparated before the Light paffes by the 
Hair, the leatl: refrangible rays, which when fepara- 
ted from the reft make red, were infleded at a greater 
diftance from the Hair, fo as to make three red fringes 
at a greater diftance from the middle of the fhadow of 
the Hair 3 and the moft refrangible rays which when 
feparated make violet, w^re inflefted at a lefs diftance 
from the Hair, fo as to make three violet fringes at a 
lefs diftance from the middle of the ftiadow of the Hair. 
And other rays of intermediate degrees of refrangibi- 
lity were infledted at intermediate diftances from the 
Hair, fo as to make friezes of intermediate Colours at 
intermediate diftances from the middle of the fhadow 
of the Hair. And in the fecond Obfervation, where 
all the Colours are mixed in the v/hite Light which 
paifes by the Hair, thefe Colours are feparated by the 
various iniiexions of the rays, and the fringes which 
they make appear all together , and the innermoft 

S s a fringes 



fringes being contiguous make one broad fringe compo- 
fed of all the Colours in due order, the violet lying 
on the infide of the fringe next the fhadow., the red on 
the outfide furtheft from the fliadow, and the blue, 
green and yellow, in the middle. And, in like man- 
ner, the middlemoft fringes of all the Colours lying iii 
order, and being contiguous, make another broad fringe 
compofed of all the Colours ; and the outmoft fringes 
of all the Colours lying in order, and being contiguous,, 
make a third broad fringe compofed of all the Colours. 
Thefe are the three fringes of coloured Light with 
which the fhadows of all Bodies are bordered in the fe- 
cond Obfervation. 

When I m^ade the foregoing Obfervations, I defigned 
to repeat moft of them with more care and exadtnefs^ 
and to make fome new ones for determining the man- 
ner how the rays of Light are bent in their paflage by 
Bodies for making the fringes of Colours with the- 
dark lines between them. But I was then interrup- 
ted, and cannot now think of taking thele things into 
further confideration. And iince 1 have not .hnifhed: 
this part of my Defign, I (hall conclude, with propo- 
fing only fome Queries in order to a further fearch ta 
be made by others. 

^ery 1 . Do not Bodies a(3 upon Light at a diftance^v 
and by their aftion bend its rays, and is not this a£tioa 
(ceteris fartim) ftrongeft at the leaft diftance? 

<%. a. Do not the rays which differ in refrangibility 
differ alfo in flexibility, and are they not by their dif- 
ferent inflexions feparated from one another , fo as 
after feparation to make the Colours in the three fringes 

above 



[133] 

above defcribed ? And after what manner are they in- 
fleifled to make thofe fringes ? 

^. 5. Are not the rays of Light in paffing by the 
edges and fides of Bodies^ bent feveral times backwards 
and forwards, with a motion like that of an Eel ? And 
do not the three frin2;es of coloured Light above-men- 
tioned, arife from three fuch bendings ? 

^, 4. Do not the rays of Light which fill upon Bo- 
dies, and are reflected or refraded, begin to bend be- 
fore they arrive at the Bodies ; and are they not re- 
flected, refracted and infleded by one and the fame 
Principle, acting varioufly in various circumftances ? 

^, 5. Do not Bodies and Light aft mutually upon 
one another, that is to fay, Bodies upon Light in emit- 
ting, reflecting, refraCting and inflefting it, and Light 
upon Bodies for heating them, and putting their parts 
into a vibrating motion wherein heatconfifts ? 

^. 6. Do not black Bodies conceive heat more eafily 
from Light than thofe of other Colours do, by reafon 
that the Light falling on them is not refleded outwards^ 
but enters the Bodies, and is often reflected and re- 
frafted within them, until it be ftifled and loft ? 

*^. 7. Is not the ftrength and vigor of the action 
between Light and fulphureous Bodies obferved above,, 
one reafon why fulphureous Bodies take fire more 
readily, and burn more vehemently, then other Bo-, 
dies do ? 

^. 8.. Do not all fixt Bodies when heated beyond a 
certain degree, emit Light and fhine, and is not this 
emifiion performed by the vibrating motions of their 

parts? v5..^5^eO*, 



[134] 

^i. 9. Is not fire a Body heated fo hot as to emit 
Light copioudy ? For what elfe is a red hot Iron than 
fire ? And what elfe is a burning Coal than red hot 
Wood ? 

c%. 10. Is not flame a vapour, fume or exhalation 
heated red hot, that is, fo hot as toihine? For Bodies 
do not flame without emitting a copious fumie, and this 
fume burns in the flame. The Ig^m Fatum is a vapour 
fliining without heat, and is there not the fame diffe- 
rence between this vapour and flame, as between rot- 
ten Wood fliining v/ithout heat and burning Coals of 
fire ? In diftilling hoj^ Spirits, if the head of the fl:iri be 
taken off, the vapo^ir which afcends out of the Still will 
take fire at the flame of a Candle, and turn into flame, 
and the name wifl riin along the vapour from the Candle 
to tlie Still. Some Bodies heated by motion or fermen- 
tation, if the heat grow intenfe fume copioufly, and if 
the heat be great enough the fumes will fliine and be- 
com.e flame. Metals in fufion do not flame for want of 
a copious fume, except Spelter which fumes copioufly, 
and thereby flames. AU flaming Bodies, as Oyl, Tal- 
low, Wax, Wood, foffil Coals, Pitch, Sulphur, by 
flaming wafl:e and vanifli into burning fmoke, which 
fmoke, af the flame be put out, is very thick and vifible, 
and fomxtimes fmefls ftrongly, but in the flame lofes 
its fmell by burning, and according to the nature of the 
fmoke the flame is of feveral Colours, as that of Sul- 
phur blue, that of Copper opened with Sublimate 
green, that of Tallow yellow. Smoke paffing through 
flame cannot but grow red hot, and red hot imoke can 
have no other appearance than that of flame. 

^, 1 1 . 



^. 1 1. Do not great Bodies conferve their heat the 
longeft, their parts heating one another, and may not 
great denfe and fix'd Bodies, when heated beyond a 
certain degree, emit Light fo copioufly, as by the emif- 
fion and readion of its l-.ight, and the reflexions and re- 
fraftions of its rays within its pores to grow ftill hot- 
ter, till it comes to a certain period of heat, fuch as is 
that of the Sun ? And are not the Sun and fix'd Stars 
great Earths vehemently hot, whofe heat is conferved 
by the greatnefs of the Bodies, and the mutual action 
and readion between them, and the Light which they 
emit, and whofe parts are kept from fuming away, not 
only by their fixity, but alfo by the vaft weight and 
denfity of the Atmofpheres incumbent upon them, and 
very ftrongly comprefling them, and condenfing the va-> 
pours and exhalations which arifefrom them? ^U-. a))ei^^, 

^. 12, Do not the rays of Light in falling upon the 
bottom of the Eye excite vibrations in the Tunico. re^ 
tina ? Which vibrations, being propagated along the 
folid fibres of the optick Nerves into the Brain, caufe 
the fenfe of feeing. For becaufe denfe Bodies conferve 
their heat a long time, and the denfeft Bodies conferve 
their heat the longeft, the vibrations of their parts are 
of a lafting nature, and therefore may be propagated^ 
along folid fibres of uniform denfe matter to a great di- 
ftance, for conveying into the Brain the impreffions 
made upon all the Organs of fenfe. For that motion; * 
which can continue long in one and the fame part of a 
Body, can be propagated a long way from one part to- 
another, fuppofing the Body homogeneal, fo that the 
motion may not be reiledted, refraded, interrupted or 
difordered by any unevemiefs of the Bodyo 



1 16 ] 

c%. 13. Do not feveral fort of rays make vibrations 
of feveral bigneflcs, which according to their bignefles 
excite feniations of feveral Colours^ much after the 
manner that the vibrations of the Air, according to their 
feveral bigneffes excite fenfations of feveral founds ? 
And particularly do not the moft refrangible rays ex- 
cite the fhorteft vibrations for making a fenfation of 
deep violet, the leaft refrangible the largeft for making 
a fenfation of deep red, and the feveral intermediate 
forts of rays, vibrations of feveral intermediate bignef- 
fes to make fenfations of the feveral intermediate Co- 
lours ? 

^i. 1 4. May not the harmony and difcord of Co- 
lours arife from the proportions of the vibrations propa- 
gated through the fibres of the optick Nerves into the 
Brain, as the harmony and difcord of founds arifes from 
the proportions of the vibrations of the Air ? For fome 
Colours are agreeable, as thofeofGold andlndico, and 
others difagree. 

^. 1 5. Are not the Species of Objefts feen with both 
Eyes united where the optick Nerves meet before 
tJiey come into the Brain, the fibres on the right fide 
of both Nerves uniting there, and after union going 
thence into the Brain in the Nerve which is on the 
right fide of the Head, and the fibres on the left fide 
of both Nerves uniting in the fame place, and after 
union going into the Brain in the Nerve which is on 
the left fide of the Head, and thefe two Nerves meet- 
ing in the Brain in fuch a manner that their fibres 
make but one entire Species or Pifture, half of which 
on the right fide of the Senforium comes from the 
right fide of both Eyes through the right fide of 

both 



[137] 

both optick Nerves to the place where the Nerves 
meet, and from thence on the right fide of the Head 
into the Brain, and the other half on the left fide of the 
Senforium comes in like manner from the left fide of 
both Eyes. For the optick Nerves of fuch Animals as 
look the fame way with both Eyes ( as of Men, Dogs, 
Sheep, Oxen, }sfc. ) meet before they come into the 
Brain, but the optick Nerves of fuch Animals as do 
not look the fame way with both Eyes (as of Fillies and 
of the Chameleon) do not meet, if I am rightly in- 
formed. 

^, 1 6. When a Man in the dark preffes either cor- 
ner of his Eye with his Finger, and turns his Eye away 
from his Finger, he will fee a Circle of Colours like 
thofe in the Feather of a Peacock's Tail ? Do not thefe 
Colours arife from fuch motions excited in the bottom 
of the Eye by the prejQTure of the Finger, as at other 
times are excited there by Light for caufing Vifion ? And 
when a Man by a ftroke upon his Eye fees a Flafli of 
Light, are not the like Motions excited in the Retina 
by the ftroke ? 



Book m. Plate I. 




^^^S- 



j^^'"!l „!^'(^;',i:;^ 1 1 [ i[ I m L m „..„.■ .i n m 1/ 



x ii i S iiin SS '""""" 



C 1 38 3 



-. ■ w» ^*. .» » ^ . ^j. 



ENUMERATIO 



LINEA 






TERTII ORDINI& 



— ^i^Wgl H I J. -I - 



[ISP 



ENUMERATIO 

LIN 




TERTII ORDINIS. 



LIneae Geometries fecundum numerum dimen- r: 
fionum aequationis qua relatio inter Ordinatas,.^"^^'^^^ ^^'° 
& Abfeiflas definitur, vel (quod perinde eft) fecun- 
dum numerum punftorum in quibus a linea reda 
fecari poffunt, optime diftinguuntur in OrdineSs 
Qua ratione linea primi Ordinis erit Refta fola, ex 
fecundi five quadratici ordinis erunt feftiones Conicae 
& Circulus, & ex tertii five cubici Ordinis Parabola 
Cubica, Parabola Neiliana, Ciflbis veterum & reli- 
qux quas hie enumerare iuicepimus. Curva autem 
primi generis, (fiquidem refta inter Curvas non eft 
numeranda) eadem eft cum. Linea fecundi Ordinis^ 
& Curva fecundi generis eadem cum Linea Ordinis 
tertii. Et Linea Ordinis infinitefimi ea eft quam 
refta in punftis infinitis fecare poteft, qualis eft Spi- 
ralis, Cyclois, Quadratrix & linea omnis quae per 
radii vel rotae revolutiones infinitas generatur. 

T t 1 Sedionum 



[ho] 

"• Sedionum Conicarum proprietates praecipuae a 

^^XX%?-' Geometris paffim traduntur. Et confimiles funt pro- 
rum comfetunt prictatcs Curvaruiii fecundi generis & reliquarum, ut 
cttrvtsfufenorum-^^ fequcnti proprietatum prascipuarum enumera- 



tione conttabit. 
III. Nam fi reflae plures parallelae & ad conicam fe- 

Curvtwurn 
€undi 

dinatdi. 



r^^)^««? A- ftionem utrinq; terminatae ducantur, reda duas ea- 
AlmameS rUiii bifccans bifecabit alias omnes,ideoq; dicitur Ih'^- 
tri^J^ertkesfen'r^QXer^^\x^^^ rcftse bifcdiae dicuntur Ordtnatim ap- 
tra.Axej. pUcat^ ^d Diametrum, & concurfus omnium Dia- 
metrorum eft Centrum figurae, & interleftio Curv^ & 
diametri Vertex nominatur, & diameter iWiAxi^ 
eft cui ordinatim applicator infiftunt ad angulos re- 
d:os. Et ad eundem modum in Curvis fecundi ge- 
neris, fi re£i:se duae qusevis parallelae ducantur occur- 
rentes Curvae in tribus punftis : reda quae ita fecat 
has parallelas ut fumma duarum partium ex uno fe- 
cantis latere ad curvam terminatarum, aequetur parti 
tertiae ex altero latere ad curvam terminatce, eodem 
modo fecabit omnes alias his parallelas curvaeq; in 
tribus punftis occurrentes redas, hoc eft, ita ut llim- 
ma partium duarum ex uno ipiius latere Temper 
aequetur parti tertis ex altero latere. Has itaq; tres 
partes quae hinc inde ^quantur, Ordinatim affli- 
catas & rectam fecantem cui ordinatim applicantur. 
T)iametrum & interfeftionem diametri & cuYVxVer" 
ticem & concurfum duarum diametrorum Centrum 
nominare licet. Diameter autem ad Ordinatas re- 
dangula fi modo aliqua fit, etiam Axis dici poteft^, 
& ubi omnes diametri in eodem pundo concurrunt 
iftud erit Centrum generate. . 

Hyper-« 



[ HI ] 

Hyperbola primi generis duas u4[fmj^totoSy ea fe- iv. 
eundi tres^ea tertii quatuor & non plures habere. 2^-'earl!m'^lpietT 
teft, & fie in reliquis. Et quemadmodum partes f^-^v-" 
lineae cujufvis refta^ inter Hyperbolam Conicam & 
duas ejus Afymptotos lunt hinc inde acquales : fie iii 
Hyperbolis fecundi geaeris fi ducaturi|:efta quaevife 
fecans tarn Curvam quam tres ejus Afymptotos in 
tribus punftis, fumma duarum partium iftius redse 
qua? a duobus quibufvis Alymptotis in eandem pla- 
gam ad duo punfta Curvge extenduntur aequalis erit 
parti tertiae quae a tertia Afymptoto iii plagam con- 
trariam ad tertium Curva? pundum extenditur. 

Et quemadmodum in Conicis feftionibus non Pa- v. 
rabolicis quadra turn Ordinatim applicatae^ hoc eil, Laterareaa^^^^- 
redtangulum Ordinatarum quae ad contrarias par-^"^ "^^ 
tes Diametri ducuntur, eft ad redangulum partium 
Diametri qu^ ad Vertices Ellipfeos vel Hyperbolas 
terminantur,ut data quaedam linea quae dicitur Latm 
• re(Hum^ ad partem diametri qus inter Vertices jacet 
& dicitur ia^m tranfverfum : fie in Curvis non Para- 
bolicis fecundi generis Parallelepipedum fub tribus 
Ordinatim applicatis eft ad Parallelepipedum fub par- 
tibus Diametri ad Ordinatas & tres Vertices figurae ab- 
fciffis, in ratione quadam data : in qua ratione fi fu- 
mantur tres reftaead tres partes diametri inter ver-- 
tices figurae fitas fingulaead fingulas, tunc ilte tres- ^ 
redas dici poflunt Later a re<Ha Rguvx^ & illae partes < 
Diametri inter Vertices Later a tranfverfa. Et ficut: 
in Parabola Conica quae ad unam & eandem diame- 
trum unicum tantum habet Verticem, reftangulum^ 
fub Ordinatis aequatur redangulo fub parte Diametri 
quae ad Ordinatas & Verticem abfcinditur & refta^ 

quadam ; 



14^ 

quadam data quae Latus reftum dicitur,fic in Curvis 
lecundi generis quas non nil! duos habent Vertices ad 
eandemDiametrum, ParallelepipedumfubOrdinatis 
tribus aequatur Parallelepipedo iub duabus partibus 
Diametri ad Ordinatas & Vertices illos duos abfciffis, 
& refta quadam data quae proinde Latm return 
dici poteft. 

VI. Deniq; ficut in Conicis fe£tionibus ubi duae paral- 
ruljulZr'Jie'^ Ick ad Curvam utrinq; terminata? fecantur a dua- 
Urumfegmemis. bus parallelis ad Curvam utrinq; terminatis, prima 

a tertia & lecunda a quarta, rectangulum partium 
primiB eft ad redangulum partium tertiae ut reftan- 
gulum partium fecundae ad reftangulum partium 
quartan : fie ubi quatuor tales redas occurrunt Curvae 
lecundi generis fingulae in tribus punftis, parallele- 
pipedum partium primae redae erit ad parallelepide- 
dum partium tertian, ut parallelepipedum partium 
fecundcE ad parallelepipedum partium quartae. 

VII. Curvarum fecundi & fuperiorum generum aeque 
^./Se^p?r£^^tq;pi"™i crura omnia in infinitum progredientia 
ika& eorum fa- yqI Hy^erMici fuut gcueris vcl Taf^dMict. Crus Hy^ 
^^' ferhoikum voco quod ad Afymptoton aliquam in in- 
finitum appropinquate Para/'<?/2r^^w quod Afymptoto 
deftituitur. Haec crura ex tangentibus optime dig- 
nofcuntur. Nam fipunftum contaftus in infinitum 
abeat tangens cruris Hyperbolici cum Afymptoto 
coincidet & tangens cruris Parabolici in infinitum 
recedet, evaneicet & nuUibi reperietur. Invenitur 
igitur Aiymptotos cruris cujufvis qua^rendo tangen- 
tem cruris illius ad pundum infinite diftans. Plaga 
autem cruris infiniti invenitur quaerendo pofitionem 
redas cujutVis quae tangenti parallela elt ubi pun- 

d»um 



[ H3 3 

ftum contaftus in infinitum abit. Nalll h^c rect^ 
in eandem plagam cum crure infinito dirigitur. 

Linear omnes Ordinis primi, tertii, quinti, fep- VIII. 
timi & imparis cujufq; duo habent ad minimum ^^f^'f;'^^^;;; 
ctura in infinitum veiius plagas oppofitas pYogYQ-s^-^ensfecwridiad 
dientia. Et line^ omnes tertii Ordinis duo habent ^^^f^^^^^f^ 
ejufmodi crura m plagas oppofitas progredientia m primus. 
quas nulla alia earum crura infinita (prasterquam 
in Parabola Cartefiana ) tendunt. Si crura ilia 
fint Hyperbolici generis , fit G A S eorum Afymp- 
totos & huic parallela agatur reda qusevis CBc 
ad Curvam utrinque ( fi fieri potefl: ) terminata 
eademq; biiecetur in pundtoX, & locus pun£ti il-^'if- r- 
lius X erit Hyperbola Conica ( puta X $ ) cujus 
una Afymptotos eft AS. Sit ejus altera Afymp- 
totos A B, &: a^quatio qua relatio inter Ordinatam 
BC & Abfciffam AB definitur, fi AB dicatur x & 
B C y^ femper induct hanc formam xyy-^-ey — ax^ 
-j^bxx-j-cx-j-d. Ubi termini e, a, b^ c, d, defig- 
nant quantitates datas cum fignis fuis -J- &— < aife- 
ftas, quarum quaellbet deeflfe poffunt modo ex earum 
defeftu figura in fedtionem conicam non vertatur.. 
Poteft autem Hyberbola ilia Conica cum afymp to- 
lls fuis coincidere^ id eft pundum X in reda AB 
locari : & tunc terminus -|-ey deeft. 

At fi reda ilia CBc non poteft utrinq; ad Cur\ram 
terminari fed Curvas in unico tantum pun£to occur- ^ r ^?~' , 

r ' 1 n \ -n r Calm ecundm, 

rit : age quamvis politione datamrectam A d aiymp- 
toto AS occurrentem in A, ut & aliam quamvis BC 
afymptoto illi parallelam CurviEque occurrentem in 
pundoC, & cequatio qua relatio inter Ordinatam 

BC 



X. 
Cafus tertms. 



XI. 

-Cajm quartm. 



144] 

BC & Abfciffam AB definitur^ femper induct hanc 
for mam x y == a x^ -|- b x x -y c x -J- d. 

Quod fi crura ilia oppofita Parabolici lint generis, 
refta CB cad Curvam utrinque, fi fieri poteft, ter^ 
minata in plagam crurum ducatur & bifecetur in B, 
& locus punSti B erit linea reda. Sit ifta AB, ter- 
minata ad datum quodvis pundum A, & oequatio 
qua relatio inter Ordinatam BC ScAbfciflam AB 
definitur, femper induct hanc formam, yy = ax^ 
^-bxx-^cx-j-d. 

At vero fi redla ilia CB c in unico tantum pundo 
occurrat Curvas, ideoq; ad Curvam utrinq; terminari 
non poflit : fit punftum illud C, & incidat reCta ilk 
ad punttum B in redam quamvis aliam pofitione 
datam & ad datum quodvis pundum A terminatam 
AB : & aequatio qua relatio inter Ordinatam BC & 
Abfciffam AC definitur femper induct hanc formam, 
y = ax^-^bxx-|-cx-i-d. 

Enumerando curvas horum cafuum, Hyperbolam 
Nominaforma- yocabimus infcrtftam quae tota jacet in Afymptot6n 
a ngulo ad inftar Hyperbolae conicae, circumjcriftam 
quae Afymptotos fecat & partes abfciffas in finu fuo 
ampleftitur, ambigenam quae uno crure infinito in- 
fcribitur & altero circumfcribitur , convergentem 
cujus crura concavitate fua feinvicem refpiciunt & 
in phg^m^^nd^mdinguntUT ^divergent em cujus crura 
convexitate fua feinvicem recipiunt & in plagas con- 
trarias diriguntur, crunbus contrariu fr^ditam cujus 
crura in partes contrarias convexa funt & in plagas 
contr^iims infiimtd.^ Conchoidalem quae vertice concavo 
& cruribus divergentibus ad afymptoton applicatur, 
anguineam quae flexibus contrariis afymptoton fecat 

& 



xn. 



rum 



[H5] . 

& utrinq; in crura contraria producitur, cfuciformem 
qua: conjugatam decuflat, nodatam qux feipfam de- 
cuffat in orbem redeundo, cujpdatam ciijus partes 
duae in angulo contadus concurrunt & ibi terminan- 
tur, funSatam quse conjugatam habet Ovalem infi- 
nite parvam id eft pun£tuni, & furam quae per im- 
poffibilitatem duarum radicum Ovali, Nodo, Cuf- 
pide & Pundo conjugate privatur. Eodem fenfu 
rarabolam quoq; convey'gentem^ divergent em^ cruri- 
hm contrarm frccditam^ cruciformeni^ nodatam^ cuj^ 
fid at am J funHatam Sl furam nominabimus. 

In calu primo fi terminus a x? affirmativus eft Fi- ™- 
gura erit Hyperbola triplex cum fex cruribus Hy- redundante'^& '^ 
perbolicis quae iuxta tres Alymptotos quarum nulte^-/^ ^^''^^ ^^ 
iunt parallelae in mfinitum progrediuntur,binae juxta^ ^ ' 
unamquamq; in plagas contrarias. Et hx Afymp- 
toti li terminus bxx non deeft fe mutuo fecabunt 
in tribus pundis triangulum (Dd^^j inter fe con- 
tinentes, fin terminus bxx deeft convergent omnes 
ad idem pundlum. In priori cafu capeAD=: 
-~, & Ad=^Ac/ = j^, ac junge Dd, Dc/^, & erunt 
AD, Ddj Dj^tres Afymptoti. In pofteriori due 
ordinatam quamvis B C, & in ea utrinq; produfta 
cape hine inde BF & Bffibi mutuo aequales & 
in ea ratione ad A B quam habet /d. ad a, j'angeq; 
AF, At% & erunt AB, AF, Af tres Alympoti. 
Hanc autem Hyperbolam vocamus redundantem 
quia nurnero crurum Hyperbolicorum Sediones Co- 
nicas fuperat. 

In Hyperbola omni redundante fi neq; terminus B^hlm Hy- 
e y defit neq; fit b b - 4 a c aequale + a e ^a curva mA-^prboU diametris 
lam habebit diametrum, fin eorum alterutrum ac- ^f^!" crumm 

U u cidat 



Gidat curva habebit unicam diametrum, & tres fi 
utrumque. Diameter autem femper tranfit per In^ 
terfeftionem duaruin Afymptoton & bilecat redas 
omnes quas ad Afymptotos illas utrinq; terminantnr 
& parallelse funt & Aiymptoto tertiae. Eftq; abfcifla 
AB diameter Figurae quoties terminus ey deeft. 
Diametrum vcro abiblute diftam hie & in fequen- 
tibus in vulgari fignificatu ufurpo, nempe pro ab- 
fcifla quae paflim habet ordinatas binas a^quales ad 
idem punftum hinc inde infiftentes. 
XV. Si Hyperbola redundans nullam habet diametrum 

^.^CJi'LTJ qu^rantur ^quationis hujus ax^-bx'+cxx-l-dx 
^m diametro de- -|- ;J = o radices quatuor feu valores ipfius x. Eae 
trrS/t;:::f"nto a P, a ^ , a , , a p. Engantur ordinate 
tos trianguium PT, -nrr, ttT, p t, & hoe tangent Curvam in punftis 
capemes,. totidcm T, r, "^ , t, & taugendo dabunt limites Cur- 

vae per quos fpecies ejus innotefcet. 
Hf. 1,2, Nam fi radices omnes AP, A*^, A^, Ap funt 

reales^ ejufdem figni & in^quales, Curva conftat ex 
tribus Hyperbolis , ( infcripta circumfcripta Sc am- 
bigena ) cum Ovali. Hyperbolarum una jacet ver- 
fus D, altera verfus d, tertia verfus ^, & Ovalis 
femper jacet intra triangulamDd^, atq; etiam in- 
ter medios limites ^ & r , in quibus utiq; tangitur 
ab ordinatis -rf^ & '^'^^ Et haec eft fpecies prima. 
^^' J, 4- Si e radicibus duae maximae Att, A f^ vel duae mi- 

nimal AP, A^ aequantur inter fe, & ejufdem funt 
figni cum alteris duobus, Ovalis & Hyperbola cir- 
cumfcripta fibi inxicem junguntur coeuntibus earum 
punftis conta£tus7 & t vel T & t, & crura Hyper- 
bolae fefe decuflando in Ovalem continuantur, iigu- 
ram nodatam efficientia* Quae fpecies eft fecunda. 

Si 



CH7] 

Si e radicibus tres maximae A/, At, A to-, vel tres fi^: 5, <?. 
minimse A tt, a te-, A P iiequentur inter fe, Nodus in 
€'ufpdem acutiffimum convertetur. Nam crura duo 
Hyperbolae circumfcriptoe ibi in angulo contaftus 
concurrent & non ultra producentur. Et haec eft 
fpecies tertia. 

Si e radicibus dua? mediae At«r ^ Att aequentur in- iFiv. 7. 
ter fe, punda contaftus t &7 coincidunt, & propte- 
rea Ovalis interjefita in punftum evanuit, & conftat 
figura ex tribus Hyperbolis, infcripta, circumfcripta 
& ambigena cum fun^o conjugato. Quae eft fpecies 
quarta. 

Si duae ex radicibus funt impoffibiles & reliquae%'7->S,s3,i4^ 
duae inaequales & ejufdem figni ( nam figna contraria 
habere nequeunt^) fur^ habebuntur Hyperbolae tres 
fine Ovali vel Nodo vel cufpide vel punfto conju- 
gato, &hae Hyperbolae vel ad latera trianguli ab 
Afymptotis comprehenfi vel ad angulos ejus jacebunt 
& perinde fpeciem vel quintam vel fextam confti« 
tuent. 

Si e radicibus duae funt sequales & alterae du3e%. 9rio^iS?J< 
vel impoffibiles funt vel reales cum fignis quae a fig- 
nis aequalium radicum diverfa funt, figura cruciform 
mis habebitur, nempe dua: ex Hyperbolis feinvicem 
decuffabunt idq; vel ad verticem trianguli ab A- 
fymptotis comprehenfi, vel ad ejus bafem. Quae 
duae fpecies funt feptima & odava. 

Si deniq; radices omnes funt impoffibiles vel fi^ir- 11512; 
omnes funt reales & in^quales & ecirum duae funt 
affirmativae & alterae duae negativae, tunc duse habe- 
buntur Hyperbolae ad angulos .oppofitos duarum 

Mu 1 -Afymp^ 



[148] 

Afymptoton cum Hyperbola anguinea circa Afymp- 
toton tertiam. Quas fpecies eft nona. 

Et hi funt omnes radicum cafus poffibiles. Nam 

fi duae radices funt aequales inter le, & aliae dua^ funt 

etiam inter fe oequales, Figura evadet Se6tio Conica 

cum linea redla. 

xVL Si Hyperbola redundans habet unicam tantum 

,^yp'''^'ff"Dmmetmm fit ejus Diameter Abfciffa AB, & aequa- 

tescnrminkatan-tiomshujus ax^ -|- bx x-j- cX'l-d^ o qusere tres ra- 

turn Diametro. ^^qq<^ fg^ valores X. 

Fig. 17. Si radices illae funt omnes reales & ejufdem figni^ 

Figura conftabit ex Ovali intra triangulum D d o'^ ja- 
cente & tribus Hyperbolis ad angulos ejus, nempe 
circumfcripta ad angulum D Sc infcriptis duabus ad 
angulos d & cT. Et haec eft fpecies decima. 

Fi^' 1^' Si radices duae majores funt aequales & tertia ejuf- 

dem figni, crura Hyperbolae jacentis verfus D fefe 
deculTabunt in forma Modi propter conta£tum Ova- 
lis. Quae fpecies eft undecima. 

F^i- ip- Si tres radices funt aequales. Hyperbola ifta fit 

cujpdata fine Ovali. Quae fpecies eft duodecima. 

fpg, 20. Si radices duae minores funt aequales & tertia ejuf- 

dem figni, Ovalis in funSium evanuit. Quae fpecies 
eft decima tertia. In fpeciebus quatuor noviffimis 
Hyperbola quae jacet verfus D Afymptotos in finu 
fuo ampleditur, reliqua^ duae in finu Afymptoton 
jacent. 

Fig. 20, Si duae ex radicibus funt impoflibiles habebuntur tres 

pfg. Ill Hyperbolae fur^ fine Ovali decuflatione vel cufpide. 

i%. 23. Et hujus cafus fpecies funt quatuor, nempe decima 

quarta fi Hyperbola circumi'cripta jacet verfus D & 

decima 



declma quinta fi Hyperbola infcripta jacetTerfus D, 
decima lexta li Hyperbola circumfcripta jacet fub 
bafid^ trianguli Dd^, & decima feptima fi Hyper- 
bola infcripta jacet fub eadem bafi. 

Si du32 radices funt oequales & tertia figni dWevfi^'^'^^- 
figura mt cruciformts, Nempe diia? ex tribus Hy- "°^^" 
perbolis leinvicem decuffabunt idq; vel ad verticem 
trianguli ab Afymptotis comprehenfi vel ad ejus ba- 
fem. Qu« duse fpecies funt decima octava Sc decima 
nona. 

Si duse radices funt inasquales & ejufdem figni & 
tertia eft figni diverfi, duac habebuntur Hyperbolae 
in oppofitis angulis duarum afymptoton cum Con^ 
choidali intermedia. Conchoidalis autem vel jace- ^^i"- ^> 
bit ad eafdem partes afymptoti fuae cum triangulo '^' ^ * 
ab afymptotis conftituto, vel ad partes contrarias j 
& hi duo cafus conftituunt fpeciem vigefimam & vi- 
gefimam primam. 

Hyperbola redundans quas habet tres diametros rr^'^lh , 
conltat ex tribus Hyperbolis m linubus alymptoton redundames cum 
jacentibus, idq; vel ad angulos trianguli ab afympto- trihmDUmetris. 
tis comprehenfi vel ad ejus latera. Cafus prior dat pfg. ip] 
fpeciem vigefimam fecundam^Sc pofterior ipeciem vi- 
gefimam tertiam. 

Si tres afymptoti in punfto communi fe mutuo xvni.' 
decuffant, vertuntur fpecies quinta & fexta in ^^g^- ^.XuXZs 
fimam quartam , feptima & odava in vigefimam cum Afym^mk 
quintam. & nona in vigefimam fextam ubi Ansuinea ^'''^^^ ^^^°^'^^- 

A f p o»«r-^^ punctum con*' 

non tranht per concurium alymptoton^ oc m vigeh- vergemibm. 
mam feptimam ubi tranfit per concurfum ilium, quo ^J^- 3o- 
cafu termmi b ac d defunt, & concurfus afympto- b|. 32*: 
ton eft centrum figuros ab omnibus ejus partibus^^-33' 

fitis 



oppofitis ^qualiter diftans. Et hse quatuor ipecies 
Diametrum non habent. 
F^' 34' Vertuntur etiam fpecies decima quarta ac decima 

§f. \l\ fata in vigefimam oCtavam^ decima quinta ac de- 

^^- 37- cima feptima in vigefimam nonam, decima odava 

& decima nona in tricefimam^ 8c vigefima cum vige- 
fima prima in tricefimam primam. Et hae fpecies 
unicam iiabent diametrum. 
F^. 3%. Ac deniq; fpecies vigefima fecunda & vigefima 

tertia vertuntur in fpeciem tricefimam fecundam cu- 
jus tres funt Diametri per concurfum alymptoton 
tranfeuntes. Quae omnesj converfiones facillime in- 
telliguntur faciendo ut triangulum ab afymptotis' 
comprehenfum diminuatur donee in punftum eva- 
nefcat. 
^ix. Si in primo sequationum cafu terminus a x^ ne- 

defr^^'^JZ g^^ivus eft, Figura erit Hyberbola defeftiva unicam 
tfrum non hahen- habcus afymptotou & duo tautum crura Hyperbo- 
^^"^° lica juxta afymptoton illam in plagas contrarias in- 

finite progredientia. Et afymptotos ilia eft Ordi- 
nata prima & principalis A G. Si terminus e y non 
deeft figura nullam habebit Diametrum, fi deeft ha- 
bebit unicam. In priori cafu fpecies fie enume- 
rantur. 
^'^l' W' Si sequationis hujus a x'* = b x^ 4- c x x -|r d x -\- ^ e e, 

radices omnes Att, AP, A/, A-nr^ funt reales & in- 
^quales, Figura erit Hyperbola anguinea afympto- 
ton flexu contrario amplexa, cum Ovali conjugata. 
Quae fpecies eft tricefima tertia. 
v%.4c. Si radices duae mediae AP & Af cequentur inter 

fe, Ovalis & Anguinea junguntur fefe decuflfantes 
m iovvm Modu Quae eft fpecies tricefima quarta. 

Si 



SI tres radices funt ^quales, Nodus vertetur m^'i^'4i» 
cuff idem acutlffiinum In vertice anguines. Et haec 
eft fpecles triceslma quinta. 

Si e tribus radicibus ejufdem fignl duae maximae ^'^' 43- 
A / Sc A -^ fibi mutuo aequantur, Ovalis in f unburn 
evanuit. Qua? fpecies eft tricefima fexta. 

Si radices duss qua^vis imaginariae funt^ fola ma- 
nebit Anguinea fura fine Ovali, decuffatione, Guf- 
pide vel puniSto conjugate. Si Anguinea ilia non%.42» 
tranfit per pundum A fpecies eft tricefima feptlma, 
fin tranfit per pundum illud A ( id quod contingit ^-^i"- 43* 
ubi termini b ac d defunt,) pundium illud A erit 
centrum figuras reftas omnes per ipfum du£tas & 
ad Curvam utrinq; terminatas bilecans, Et haec 
eft fpecies tricefima oftava. 

In altero cafu ubi terminus ey deeft Sc propterea xx; 
figiira Diametrum habet, fi aequatlonls hujus ^'^' tem^mivlli- 

= bxX-|-CX-|-d radices omnes AT^ Atj At, {uut ametrum hdln^ 

realeSj inaequales & ejufdem fignl, figura erit Hyper- ^5" 
bola Conchoidalis cum Ovali ad convexitatem. Quae ' "*" \ 
eft fpecies tricefima nona. 

Si duae radices funt inaequales & ejufdem fignl &%-44' 
tertia eft figni contrarii, Ovalis jacebit ad concavi- 
tatem Conchoidalis. Eftq; fpecies quadragefima. 

Si radices duae minores AT, At, funt aequales =%, 4^, 
& tertia At eft ejufdem figni, Ovalis & Conchoi- 
dalis jungentur fefe decuffando in modum Modi. 
Quae fpecies eft quadragefima prima. 

Si tres radices funt aequales, Nodus mutabitur inHf^47> 
Cuffidem & figura erit CiJJ^ois P^eterum. Et haec eft 
fpecies quadragefima fecunda. 



C 1^2 ] 

3%-. 49. Si radices duae majores funt aequales, Sc tcrtia eft 

cjufdem figni^Conchoidalis habebit fun6lum conju- 
gatuin ad convexitatem fuam^ eftq; fpecies quadra- 
gefima tertla. 
Fi^. 4p: Si radices duae funt aequales & tertia eft figni con- 

trarii Conchoidalis habebit funSum conjugatum 
ad concavitatem luam, eftq; fpecies quadragefima 
quarta. 
.:i7f..48,49. Si radices duae funt impoflibiles habebitur Con- 

choidalis furct fine Ovali , Nodo , Cufpide vel 
pun£to conjugate. Quae Ipecies eft quadragefima 
quinta. 
XXI. Siquando in primo aequationum cafu terminus a x^ 

tem^plMki' ^^^^ & terminus bxx non deeft, Figura erit Hy- 
Diamemm non perbola ParaboHca duo habens crura Hyperbolica ad 
hahenm. uuam Afymptoton SAG & duo Parabolica in pla- 

gam unam & eandem convergentia. Si terminus 
ey non deeft figura nuUam habebit diametrum, fin 
deeft habebit unicam. In priori cafu fpecies funt 
hse. 
.■Tig.^oZ Si tres radices AP, kt^^ At aequationis hujus 

bx^-j-cx ^-dx-|-^ ee==o funt inaequales & ejufdem 
figni, figura conftabit cxOvali ScaUis duabus Curvis 
quae partim HyperboHcae funt & partim ParaboHca. 
Nempe crura ParaboHca continuo du£tu junguntur 
eruribus HyperboHcis fibi proximis. Et haec eft 
fpecies quadregefima lexta. 
.^^.5=1. Si radices duae minores funt aequales Sc tertia eft 

ejufdem figni, Ovahs & una Curvarum illarum 
Hyperbolo-ParaboUcarum. junguntur &: fe deculTant 
in formam Nodi, Qjax Ipecies eft quadragefima 
feptima. 

Si 



Si tres radices funt irquales, Nodus ille in Cuf-F/^. 51. 
pidem veititur. Eftq;fpecies quadragefima oftava. 

Si radices duae inajores iunt aequales & tertia eft ^^^i- S3- 
ejufdem iigni-, Ovalis in. funclum conjugatum eva- 
nuit. QviX fpecies eft quadragefima nona. 

Si duce radices ilant impoiiibiles^ manebmit y?<r^%- S3,54« 
ilte dus curva: Hyperbolo-parabolicge fine Ovali, 
dectiflation e^cufpide vel punfto conjugato, & fpe- 
ciem quill quagefimam conftituent. 

Si radices duae funtsequales & tertia eft figni con- ^''^" ^^^ 
trarii, Curvoe ilte hyperboio-parabolicae junguntur 
fefe decuffando in morem crucis. Eftq; fpecies quin- 
quagefima prima. 

Si radices duas funt inaequales & ejufdem figni & ^'^' '^^- 
tertia eft figni contrarii, figura evadet Hyperbola 
anguinea circa Afymptoton AG, cum Parabola con- 
jugata. Et haec eft fpecies quinquagefima fecunda. 

In altero cafu ubi terminus ey deeft & figura ^™- 
Diametrum habet, fi duse radices aequationis hujus tmrTarlboikt 
b X x-J- c x-j- d = o funt impoffibileSj duae habentur ^i^metrum ha- 
figurse hyperbolo-parabolicae a Diametro A B hinc fZ%j. 
inde aequaliter diftantes. Quae fpecies eft quinqua- 
gefima tertia. 

Si aequationis iliius radices duae funt impoffibiies, %' S§* 
Figurae hyperbolo-parabolicae junguntur fefe de- 
cuffantes in morem crucis, & fpeciem quinquagefi- 
mam quartam conftituunt. 

Si radices illae funt inaequales & ejufdem figni, ha- ^'^- !^^ 
betur Hyperbola Conchoidalis cum Parabola ex 
eodem latere Afymptoti» Eftq; fpecies quinquage^- 
fimaquinta« 



X 



X 



[154] 

ng.eol Si radices ilk funt figni contrarii, habetur Con- 

choidalis cum Parabola ad alteras partes Afymptoti. 

Quae fpecies eft quinquagefima fexta. 

xxiii. Siquando in primo sequationum cafu terminus 

Oumior Hy- ^terq ; ax' &bxx deeft, figura erit Hyperbolifmus 

hu. ^^ feftionis ahcujus Conicae. Hyperbolifmum figure 

voco cujus Ordinataproditapplicandocontentumfub 

Ordinata figurse illius & reda data ad Abfciflam com<«^ 

munem. Hac ratione linea refta vertitur in hyper- 

bolam Conicam, & feSio omnis Conica v^titur in 

^ aliquam figurarum quas hie Hyperbolifmos leaio- 

num Conicarum voco. Nam aequatio ad figuras 

de quibus animus, nempe xyy -|-ey-cx-|-d^ feu 

_ etA^ee'i"4dx -|- 4 cxx generatur appli- 

cando contentum fub Ordinata fe£tionis Conicae 
e4A^ee-l-4dx'|-4cxx & re£ta data m ad curvarum 

Abfciflam communem x. Unde liquet quod figura 
genita Hyperbolifmus erit Hyperbola?, Ellipfeos vel 
Parabolae perinde ut terminus ex affirmativus eft 
¥el negativus vel nullus. 

Hyperbolifmus Hyperbolae tres habet afymptotos 
quarum una eft Ordinata prima & principalis A d, 
alterae duae funt parallelse Abfciffae A B «& ab eadem 
hinc inde sequaliter diftant. In Ordinata principal! 
Ad cape Ad, A^ hinc inde ^quales quantitati /^c 
& per pun£ta d ac ^ age d g, ^7 Afymptotos Ab- 
fciflae A B parallelas. 

Ubi terminus ey non deeft figura nullam ha- 
bet diametrum. In hoc cafu fi sequationis hujus 
c x x -|- d X 'Y ;e e ==^o radices duce A P, Af funt r eales 

& 



c 155 ] 

oc ina'quales ( nam aequales effe nequeunt miiBgm3.P^i*<su 
lit Conica feftio ) figura conftabit ex tribus Hyper- 
bolis fibi oppoiitis quarum una jacet inter afymp- 
totos parallelas & alterae duae jacent extra. Et haec 
eft fpecies quinquagefima feptima. 

Si radices illoe duae lunt impoffibiles^habentur Hy- 
perbolae duae oppofitae extra alymptotos paralleks & 
Anguinea hyperbolica intra eafdern. Haec figura 
duarum eft fpecierum. Nam centrum non habet%-<^2.j 
ubi terminus d non deeft ; fed fi terminus ille deeft '^' ^^^ 
punftum A eft ejus centrum. Prior fpecies eft quin« 
quagefima oCtava, pofterior quinquagefima nona. 

Quod fi terminus e y deeft, figura conftabit ex Fig. 642 
tribus hyperbolis oppofitis quarum una jacet inter 
Efymptotos parallelas & alterae duse jacent extra ut 
in fpecie quinquagefima quarta, & praeterea diame- 
trum habet quae eft abfciffa AB. Et haec eft fpecies 
fexagefima. 

Hyperbolifmus Ellipfeos per hanc aequationem de- xxiv: 
finitur X y y + e y = c X -|- d, & unicam habet afymp- ^^^ „-^^^^^^^'^^ 
toton qus eft Ordmata prmcipalis Ad. Si termmus Fig. 6%. 
ey non deeft, figura eft Hyperbola anguinea fine dia- 
metro atq; etiam fine centro fi terminus d non deeft » 
Quae fpeeies eft fexagefima prima. 

At fi terminus d deeft, figura habet centrum fine ^^i^^tf^r 
diametro & centrum ejus eft punftum A. Species 
vero eft fexagefima fecunda. 

Et fi terminus ey deeft & terminus d non deeft^^^^'^T^^ 
figura eft Conchoidalis ad afymptoton A G, habetq j 
diametrum fine centro, & diameter ejus eft Abfciffa 
A B. Quae fpecies eft fexagefima tertia. 

X x 2 Hyper- 



[15^ J 

XXV. Hyperboliimus Parabolae per hanc aeqiiationem^ 
lifm^'p^i^' definitur x y y -|- e y ^ d ; & duas habet aiymptotos^. 

Abfciffam AB & Ordinatam primam & principalem 
A G. Hyperbolae vero in hac figura funt duge, non 
in aiymptoton angulis oppofitis fed in angulis qui 

Bv.(58. funt deinceps jacentes, idq; ad utrumq; latus ab- 

feiflk A B^ & vel fine diametro fi terminus e y ha- 

fzv. 6p. betur, vel cum diametro fi terminus ilie deeft. Qua? 

duae fpecies funt fexagefima quarta & fexagefima. 
quinta. 

XXVI. In. fecundo aequationum cafu habebatur asquatio- 
Tndens. xy = ax^-|-bxx-|-cx-|-d. Et figura in hoc cafu. 

habet quatuor crura infinita quorum duo funt hy- 

perbolica circa afymptoton A G in contrarias partes 

tendentia & duo Parabolica convergentia & cum 

prioribus fpeciem Tridentis fere efformantia. Eftq; 

%. 7<y. haec Figura Parabola ilia per quam Cartefius aequa- 

tiones fex dimenfionum conftruxit* Haec eft igitur 

fpecies fexagefima fexta. 

xxvii. In tertio cafu aequatio eratyy = ax^-[-bxx-|-cx 

TatahoUqmn- \.A & Parabolcim defio;nat cuius crura divergunt 

que dtvergtntes. 1.^. o* • ' r • 

ab invicem oc m contrarias partes mnnite progre- 
diuntur. Abfcifla AB eft ejus diameter & fpecies ejus 
funt quinq; fequentes. 
f^^' 70,71. Si3equationisax^-l-bx^-l-cx^-d=o radices om- 

nes At f AT5 At funt reales & in^equales^ figura eft 
Parabola divergens campaniformis cum Ovali ad 
verticem« Et fpecies eft fexagefima feptima. 
Bg, 72. Si radices duae funt aequales. Parabola prodit vel 

%• 73- nodata contingendo Ovalem, vel funBata ob Ovalem 

infinite parvam. Quae duae fpecies funt fexagefima 
o£tava & fexagefima nona* 

Si 



Si tres radices llint a'quales Parabola erk cufp-J^'^^-j^ 
data in vevticc. Et haec eft Parabola Neiliana qiice 
vulgQ iemlcubica dicitur. 

Si radices duse funt impoffibiles^ habetur Parabola fi^. 73, 74.. 
pura campaniformis fpeciem feptuagefiinam primam 
conftituens. 

In quarto cafu aequato erat y — ax -l-bxx-j-cx xxviii. 
'4-d, & hsc i]equatio Parabolam illam IValli/mnam ^^'""^'^f ''■^^'''' 
defignat quae crura habet contraria & cubic a di- '^' 
ci iblet. Et fie fpecies omnino funt feptuaginta 
duae,- 

Si in planum infinitum a pundo lucido illumina- ^^}\' 
tum umbr^ figurarum projiciantur, umbras fed:io-'^^^p^^'j,;^^^-^,v 
numConicarum femper erunt fediones Conical, eas 
Curvarum fecundi generis femper erunt Curvae fe- 
cundi generis^, eae curvarum tertii generis femper 
erunt Curvae tertii generis, & ficdeinceps in infini- 
tum. Et quemadmodum Circulus umbram proji- 
ciendo generat fe£tiones omnes conicas, fie Parabolse 
quinq; divergentes umbris fuis generant & exhi- 
bent alias omnes fecundi generis curvas ^ & fie 
Curv^ quaedam fimpliciores aliorum generum inve- 
niri poffunt quae alias omnes eorundem generum 
curvas umbris fuis a punfto lucido in planum pro^ 
jeftis formabunt. . 

Diximus Curvas fecundi generis a llnea refta in xxx. 
punctis tribus iecari polie. riorum duo nonnun^ ^^ ^w/e-/^; ^ 
quam coincidunt lit cum re£ta per Ovalem infi- 
nite parvam' tranfit vel per concurfum duarum par- 
tium Curvae fe mutuo fecantium vel in cufpidem 
coeuntium ducitur. Et fiquando reftae omnes in 

plagam 



plagam cruris aliciijus infiniti tendentes Curvam 
in nnico tantiim punfto lecant ( ut fit in ordinatis 
Parabolae Cartefianae & Parabolge cubical, nee non in 
re£tis Abfcifife Hyperbolifraorum Hyberbolge & Para- 
bolae pkrallelis ) concipiendum eft quod redtae illae 
per alia duo Curvati pun£ta ad infinitam diftan- 
tiam fita ( ut ita dicam ) tranfeunt. Hujufmodi 
interfettiones duas coincidentes five ad firiitam 
fint diftantiam five ad infinitam, vocabimus pun- 
dum duplex. Curvse autem quae^ habent pun- 
ftum duplex defcribi poffunt per fequ^ntia Theo- 
remata» 



I . Si anguliduo magnitudine dati PAD, PBD circa 



nica. 
Fig, 78. 



XXXL 
Hoeoremata de 
CiiYvarum de- - j^, 1 ""a -n a ' 

fcriftiom orga- polos pofitione datos A, B rotentur, & eorum crura 
A P, B P concurfu fuo P percurrant lineam re6tam ; 
crura duo reliqua A D, B D concurfu fuo D defcri- 
bent feftionem Conicam per polos A, B tranfeun- 
tern : praeterquam ubi linea ilia reda tranfit per po- 
lorum alterutrum A vel B, vel anguliBAD, ABD 
fimul evanefcunt, quibus in cafibus pundum D de- 
fcribet lineam reftam. 

1. Si crura prima A P, B P concurfu fuo P 
percurrant fe£t:ionem Conicam per polum alter- 
utrum A tranfeuntem, crura duo reliqua AD, B D 
concurfu fuo D defcribent Curvam fecundi gene- 
ris per polum alterum B tranfeuntem & pun- 
ctum duplex habentem in polo primo A per quem 
feSio Conica tranfit : prasterquam ubi anguli 
BAD, ABD fimul evanefcunt, quo cafu pun- 

6tum 



£tum D defcribet aliam fedtionem Conlcam per po- 
lum A tranfeuntem. 

3. At fi feftio Conica quam punftum P percur- 
rit tranfeat per neutrum polorum A, B, pundura 
D defcribet curvam fecund i vel tertii generis pun- 
dum duplex habentem. Et punftum illud duplex 
in concurfu crurum defcribentiuin, AD, BD in- 
venietur ubi anguliBAP, ABP limul evanefcunt. 
Curva autem defcripta fecundi erit generis fi an- 
guli BAD, ABD iimul evanefcunt, alias erit ter- 
tii generis & alia duo habebit punfta duplicia in 
polls A & B, 

Jam fedio Conica determinatur ex datis ejus xxxii. 
punais quinq; & per cadem fic defcribi poteft. ^i^'T^^ 
Dentur ejus punda quinq; A, B, C, D, E. ]un- tio per data qmn^ 
gantur eoruni tria qucevis A, B, C & trianguli ABC ^'''^'''''^^^ 
rotentur anguli duo quivis CAB, CBA circa ver- 
tices fuos A & B, & ubi crurum AC, BC interfedio 
Cfucceffive applicatur ad pundaduo reliquaD,E5 
incidat interfedio crurum reliquorumAB & BA 
in punda P & Q. Agatur & infinite producatur 
redaPQ, & anguli mobiles ita rotentur ut inter- 
fedio crurum AB, BA percurrat redam PQ, & 
crurum reliquorum interfedio C defcribet propofi- 
tam fedionem Conicam per Theorema primum. 

XXXIIL 
/-^ r* 1 • * n If Curvariim /e- 

Curvse omnes lecundi generis punctum dupltXctmdige^erisptm- 
habentes determinantur ex datis earum pundis f ^'^. ^^^^^ ^^" 

z'. _n a, 'Hill bentiiim defer Ip-^ 

leptem, quorum mium elt punctum illud dw^ltyi^ tio per data fJp^ 



[ i6o ] 

& per eadem punfta lie deicribi poiTunt. Dentui 

'Curv^ defcribenda^ pundla quselibet feptem A, B, C, 

D, E, F, G quorum A eft punftum duplex. Jun- 

gantur pundum A & alia duo qusevis e pundls puta 

;B & C ; Sc trianguli ABC rotetur turn angulus 

CAB circa verticem fuum A, turn angulorum reli- 

quorum alteruter ABC circa verticem fuum B. Et 

ubi crurum AC, BC concurfus C fucceffive appli- 

catur ad punfta quatuor reliqua D, E, F, G incidat 

concurfus crurum reliquorum A B & B A in punda 

quatuor P, Q, R, S. Per punda ilia quatuor & 

quintum A defcribatur fe61:io Conica, & anguli prae- 

fati CAB, CBA ita rotentur ut crurum A B, B A 

concurfus percurrat feftionem illam Conicam , & 

concurfus reliquorum crurum A C, B C defcribet 

Curvam propoiitam per Theorema fecundum. 

Si vice pun£ti C datur pofitione reda B C quae 
Curvam defcribendam tangit inB, lineis AD, AP 
coincident, & vice anguli DAP habebitur linea reda 
circa polum A rotanda. 

Si pun£tum duplex A infinite diftat debebit Reda 
ad plagam pundi illius perpetuo dirigi & motu pa- 
rallelo ferri interea dum angulus ABC circa polum 
;B rotatur. 

Defcribi etiam poflunt hae curvae paulo aliter per 
Theorema tertium, fed defcriptionem fimpliciorem 
pofuiffe fufficit. 

Eadem methodo Curvas tertii, quarti & fuperio- 
rum generum defcribere licet, non omnes quidem 
fed quotquot ratione aliqua commoda per motum 
localem defcribi poflunt. Nam curvam aliquam 

fecundi 



[l^l] 

iecundi vel fupeiiorls generis pundum duplex noii 
habentem comnK)de defcribere Problema eft inter 
difficiliora numerandum. 

Curvarum ufus in Geometria eft ut per earum xxxiv. 
interfediones Problemata folvantur. Proponatur ciuaHo!Z%lZ 
iEquatio conftruenda dimenfionum novem y^^'^-\-h^'^ f^^iftionemCur- 
-j- c x^ -\- d x^ \ e xH f x3 -)- g X X -]- h X -j- k = o. Ubi ''^''''^• 

b, c, d, 15c. fignificant quantitates quafvis datas 
lignis fuis 4" & -^ affectas. Aflumatur sequatio ad 
Parabolam cubicam x^ = y, & aequatio prior, fcri- 
bendo y pro x', evadet y''|"bxyy-|- cyy-j^ dxxy 
--r e X y -j- m y \- fx^ -j-g x x -j- h x -j-k = o, oequatio ad 
Curvam aliam fecundi generis. Ubi m vel f deefle 
poteft vel pro lubitu aflumi. Et per harum Curva- 
rum defcriptiones & interfediones dabuntur radices 
aequationis conftruendae. Parabolam cubicam femel 
defcribere fufficit. 

Si aequatio conftruenda per defectum duorum ter- 
minorum ultimorum hx & k reducatur ad feptem 
dimenfiones, Curva altera delendo m, habebit pun- 
dum duplex in principio abfciflae, & inde facile de-* 
fcribi poteft ut fupra. 

Si aequatio conftruenda per defedum termino- 
rum trium ultimorum gxx-i-hx-Hk reducatur ad 
fex dimenfiones , Curva altera delendo f evadet 
fedio Conica. 

Et ft per defedum fex ultimorum terminorum 
Gequatio conftruenda reducatur ad tres dimenfiones^ 
incidetur in conftrudionem JVallifianam per Para- 
bolam cubicam & lineam reftam. 

Yy Coii^ 



[ t<^2 ] 

Conftrui etiam pofiiint a^quatlones per Hyperbo- 
Urmum Parabolce cum diainetro. lit fi conftruenda 
fit hcEC asquatio dimeniionum novem termiiio penul- 
timo carens, a'^-cxx-j-dx^'i-ex^-x-fx -j-gx^^-j-hx^ 

+ m 
^-kx^-V-lx^ = o ; affumatur a^quatio ad Hyperbolif-^ 
mum ilium xxy= i, & fcribendo y pro ^, sequatio 
conftruenda vertetur in banc ay^ i-c y y + d x yy -j- e y 
-j- fxy-j-m XX y-\-g-|-hx'Hk xx-j- 1x3 = 0, quae cur- 
vam fecundi generis defignat cujus defcriptione 
Problema folvetur. Et quantitatum m ac g alter- 
utra hie deeffe poteft, vel pro lubitu aflumi. 

Per Parabolam cubicam & Curvas tertii generis 
conftruuntur etiam a?quationes omnes dimenfionum 
non plufquam duodecim, & per eandem Parabolam 
& curvas quarti generis conftruuntur omnes dimen- 
fionum non plufquam quindecim, Et fie deinceps in. 
infinitum. Et curvae illas tertii quarti & fiiperiorum 
generum defcribi femper poffunt inveniendo eorum> 
pun£ta per Geometriam planam. Ut fi conftruenda 
fit aequatiox" ^ +ax^°+bx9+cx^+dx7-j-ex^-l-fx^ 
4-gx^-|-hx5'^ixx-l- kx -|- 1 = , & defcripta 
liabeatur Parabola Cubica ; fit aequatio ad Pa- 
rabolam illarn cubicam x^ =: y ^ & fcribendo y 
pro x^ aequatio conftruenda vertetur in hane 
y4 '|-axy^ ^|-cxxyy -f^fxxy -^ixx^o , quae eft 
Arh +dx +g^ -V^^ 

sequatio ad Curvam tertii generis cujus defcriptione 
Problema folvetur. Defcribi autem poteft hsecCurva 
inveniendo ejus punfta per Geometriam planam,prop- 
terea quod indeterminata quantitas x non nifi ad 
duas dimenfiones afcendit. 



( (/nmru/ji TalrJ. 




LuruarunvTab. H. 




Cui^mnun Tahlll. 




( iirndruni 7alin^ 




( itrvaruni Tab. T 




( ({/iranim Talr VI. 

G 






Ct 


/ 






y . 






/ 


72 




r 


7;^ 




c/ 


74 


1 


fl. 


Xt/ 


B 


A 


/'/- 


IB 


t(l 


B 


L. 


\ 
















\ 


\ 






\ 






"\ 




TRACTATUS 



D E 



Quadratura Ciirvarmn. 



Yy 2 



1 1^$ ] 



wil l ' " > '-»->X f'^m^mm 



INTRODUCTIO- 



QUantitates Mathematicas non ut ex partibus 
quam minimis conftantes, fed ut motu conti- 
nuo defcriptas hie conlidero. Lineae delcri- 
buntur ac defcribendo generantur non per appofi- 
tionem partium fed per motum continuimi pun£to- 
rmn, fuperficies per motum linearum, folida per 
motum fuperficierum, anguli per rotationem late- 
rum, tempora per fluxum continuum, & fie in cae- 
teris. Hx Genefes in rerum natura locum vere ha- 
bent & in motu corporum quotidie cernuntur. Et 
ad hunc modum Veteres ducendo redtas mobiles in 
longitudinem reftarum immobilium genefin docue- 
runt redangulorum. 

Confiderando igitur quod quantitates aequalibus 
temporibus crefcentes & crefcendo genitae, pro velo» 
citate majori vel minori qua crefcunt ac generantur, 
evadunt majores vel minores j methodum quaerebam 



determinandi quantitates ex velocitalibus motuum 
vel incrementorum quibus generantur j & has mo- 
tuum vel incrementorum velocitates nominando Flu- 
xtones & quantitates genitas nominando Fluent es^ in- 
cidi paulatim^wm i665&i666in Methodum Flu- 
xionum qua hie ufus fum in Quadratura Curvarum. 

Fluxiones funt quam proxime ut Fluentium aug- 
menta sequalibus temporis particulis quam minimis 
genita, & ut accurate loquar, funt in prima ratione 
. augmentorum nafcentium ; exponi autem poffunt per 
Jineas quafcunq; quae funt ipfis proportionales. Ut 
-"^V. I, fiaregeABC, ABDG Ordinatis BC, BD fuper 

ball A B uniformi cum motu progredientibus defcri- 
bantur, harum arearum fluxiones erunt inter fe ut 
Ordinate defcribentes BC & BD, & per Ordinatas 
illas exponi poffunt, propterea quod Ordinatae illa^ 
funt ut arearum augmenta nafcentia. Progre- 
diatur Ordinata BC de loco fuo BC in locum 
quemvis novum b c. Compleatur parallelogram- 
mum BCEb, ac ducatur refta VTH quae Cur- 
vam tangat in C ipfifq; b c ScBAproduSis occur- 
rat in T & V : & Abfciff^ AB, Ordinatse BC, & 
Lineae Curva: A C c augmenta modo genita erunt 
Bb, Ec & Cc; & in horum augmentorum nafcen- 
tium ratione prima funt latera trianguli CET,ideoq; 
fluxiones ipfarum AB, BC & AC funt ut trianguli 
illius CET latera CE, ET & CT & per eadem 
latera exponi poffunt, vel quod perinde eft per la- 
tera trianguli confimilis VBC« 

Eodem recidit li fumantur fluxiones in ultima 
iiatione partium evanefcentium. Agatur refta Cc 
-& producatur eadem ad K. Redeat Ordinata be 

in 



in locum fuum priorem B C, & coeuntibus punftis 
C & c, refta CK coincidet cum tangente CH^ & 
triangulum evanefcens CEc in ultima fua forma 
evadet fimile triangulo GET, & ejus latera evanef- 
centia CE^ Ec & Cc erunt ultimo inter feut funt 
trianguli alterius GET latera GE, ET &GT, & 
propterea in hac ratione funt fluxiones linearum A B, 
BG «& AG. Si pun£ta G & c parvo quovis inter- 
vallo ab invicem diftant reda G K parvo intervallo a 
tangente GH diftabit. lit recta CK cum tangente 
G H coincidat & rationes ultimse linearum G E, E c & 
Gc inveniantur, debent pundta G & c coire & om- 
nino coincidere. Errores quam minimi in rebus 
mathematicis non funt contemnendi. 

Simili argumento fi circulus centro B radio B G 
defcriptus in longitudinemAbfciffse AB ad angulos 
reftos uniformi cum motu ducatur^ fluxio folidi ge- 
niti ABG erit ut circulus ille generans, & fluxio fu- 
perficiei ejus erit ut perimeter Girculi illius & 
fluxio lineae curvse A G conjunftim. Nam quo tem- 
pore folidum ABG generatur ducendo circulum 
ilium in longitudinem Abfcilfe A B, eodem fuper- 
ficies ejus generatur ducendo perimetrum circuli il- 
lius in longitudinem Gurvae A G. 

R^^a TB circa plum datum T revolvens fecet aliam Tig 
fofitione datam rei^amAB: qu^ritur froprtio fluxio^- 
num reBarum iUarum j4B !5 P5» Progrediatur 
refta PB de loco fuo PB in locum novum Pk In 
P b capiatur P G ipii P B aequalis, & ad A B ducatur 
P D fie, ut angulus b P D sequalis fit angulo b B G ^ 
& ob fimilitudmem triangulorum bBG, bPDerit 
augmentum Bb ad augmentum Cb ut Pb ad Db, 

Redeat 



[ 1^8 ] 

Redeat jam Pb in locum fuum piiorem PB ut aug- 
menta ilia evanefcant, & evaneicentium ratio ulti- 
ma, id eft ratio ultima Pb ad Db, ea erit quae eft 
-PB ad D B, exiftente angulo PDB refto, & prop- 
terea in hac ratione eft tluxlo ipfius A B ad fluxionem 
ipfius P B. 

Re(^a T B circa datum Tolum T revolvens fecet 
aliojs dim fofitione datas redJas ABh' AE in B b* 
E : quc^ntur p'^ofortio jluxionum re^ay-um iUarum 
A B '^ AE. Progrediatur refta revolvens P B de 
loco fuo P B in locum novum P b reflas A B, A E in 
pundis b &e fecantem, & re£tce AE parallela BC 
ducatur ipfi Pb occurrens in C, Sc erit Bb ad BC ut 
Ab ad Ae, & BC ad Eeut P B ad P E, & conjunftis 
rationibus Bb ad Ee ut AbxPB ad AexPE» 
Redeat jam linea Pb in locum fuum priorem PB, &: 
augmentum evanefcens Bb erit ad augmentum eva- 
nefcens Ee ut ABxPB ad AExPE, ideoq; in 
hac ratione eft fluxio redae A B ad fluxionem reftcs 
A E. 

Hinc C refta revolvens PB lineas qualvis Curvas 
pofitione datas fecet in pun6tis B & E, & re^ta? jam 
mobiles AB,AE Curvas illas tangant in Seftionum 
punftis B & E : erit fluxio Curvas quam refta, A B 
tangit ad fluxionem Curvae quam refta AE tangit 
utABxPB ad AExPE. Id quod etiam eveniet 
fl reda P B Curvam aliquam pofitione datam perpe- 
tuo tangat in punfto mobili P. 

Fluat quant'it/18 x uniformiter }^ invenienda/it fluxio 
qMantitatts x^. Quo tempore quantitas x fluendo 

evadit x-j-o, quantitas x^ evadet x-|-ol"^ id eft 
jper metliodum ferierum infinitarum, x''-] nox""^ 



Lj-^^i^oox^^-Mlfy^:'. Et augmenta o & nox^-M^"oox*'^ 
^-to'^r.funt adinvicem ut i & nx"-'~|-Hi^ox"-^-j-. Jc;^. 
Evanefcant jam augmenta ilia , & eorum ratio 
ultima erit i ad nx"'^ : ideoq; fluxio quantitatis 
X eft ad fluxionem quantitatis x" ut i ad nx'^"^ 

Similibus argumentis per methodum rationum 
primarum & ultimarum colligi poffiint fluxiones li- 
nearum feu redtarum feu curvarum in cafibus qui- 
bufcunque, ut & fluxiones fuperficierum, anguio- 
rum & aliarum quantitatum. In finitis autem quan- 
titatibus Analyfin fie inftituere, & finitarum nafcen- 
tium vel evanefcentium rationes primas vel ultimas 
inveftigare, confonum eft Geometriae Veterum : & 
volui oftendere quod in Methodo Fluxionum norl 
opus fit figuras infinite parvas in Geometriam intro- 
ducere. Peragi tamen poteft Analyfis in figuris qui- 
bufcunq; feu finitis feu infinite parvis quae figuris 
evanefcentibus finguntur fimiles, ut & in figuris quae 
pro infinite parvis haberi folent^ modo caute pro- 
cedas. 

Ex Fluxionibus in venire Fluentes Problema dif- 
ficilius eft, & folutionis primus gradus aequipollet 
Quadraturae Curvarum : de qua fequentia olim 



JLt Z xJ Ju< 



[lyo] 



JL xv A Cj 1 Ax LI w3 

D E 

Quadratura Curvarum. 

QUantitates indetermihatas ut motu perpetuo j 
. crefcentes vel decrefcentes, id eft ut fluen- ] 
tes vel defluentes in fequentibus confidero^defignoq; 
Uteris z, y, x, v, & earum fluxiones feu celeritates 

crefcendi noto iifdem Uteris pun£tatis z, y, x^ v. 
Sunt & harum fluxionum fluxiones feu mutationes 
magis aut minus celeres quas ipfarum z, y, x^ v 
fluxiones fecundas nominare licet & fie dignare 

Zj y, X, V, & harum fluxiones primas feu ipfarum : 

Zj y, X, V fluxiones tertias fie z^ y, x, v, & quartas fie 

z, y, x, Ve / Et quemadmodum z, y, x^ v funt flu- 

xiones quantitatum z, y, x^ v, & hae funt fluxiones 

quantitatum z, y, Xj v & hae funt fluxiones quantita- 
tum primarum z, y^x, V : fie hae quantitates confide- 
rari poITurit ut fluxiones aliarum quas fie defignabo. 



^7 



z, y, X, V, & hae ut fluxiones aliarum z, y, x, v, & 

hx ut fluxiones aliarum z, y, x, v. Defignant igitur 
II I ..«••♦• ...» ft . 

z, z, z, z, z, Z-, z, z to'r. feriem quantitatum quarum 
quGelibet pofterior eft fluxio prsecedentis & quaelibet 
prior eft fluens quantitas fluxionem habens fubfe- 

quentem. Similis eft feries /^az— zz, ^^az— zz, 

f/?iz—zz , /^az— zz , >^az— zz ^ /^az— zz , ut & 

^ ^. az-4-z^ az-\-z^ az-pz^ az-|-z^ az^-z^ 



a z ai~'^"°°z d z a z a z 

a -l-^^ ^ 

.^ J...-__ . Et notandum eft quod quantitas quaelibet 



a— z 



prior in his feriebus eft ut area figurae curviliniae 
cujus ordinatim applicata reftangula eft quantitas 

pofterior & abfcifla eft z : uti /^az-==-zz area curvge 

cujus ordinata eft /^az— zz & abfcifla z. Quo au^ 
tern fpeftant hsec omnia patebit in Propofitionibus 
quae fequuntuia 



P R O P, 



C 172 3 

PROP. I. PROB. L 

^ata ^equatione quotcunq* fluent es quantitates invoU 
vente^ invenire fiuxiones, 

Solutio. 

Multipllcetur omnis aequatlonis terminus per in- 
dicem dignitatis quantitatis cujufq; fluentis quam 
involvit, & in fingulis multiplicationibus mutetur 
dignitatis latus in fluxionem fuam, & aggrega- 
turn faftorum omnium fub propriis fignis erit 
aequatio nova. 

Expltcatio. 

Sunto a, b^ c, d Is)'^. quantitates determinata? & 
immutabiles, & proponatur aequatio quaevis quan- 
titates fluentes z, y, x '^c, in volvens^ uti x^ — x y y 
-|- a a z — b^ = o. Multiplicentur termini primo per 
indices dignitatum x, & in fingulis multiplicationi- 
bus pro dignitatis latere, feu x unius dimenfionis, 

fcribatur X5& fumma fadorum erit 3 x x' — x y y .Idem 
fiat in y & prodibit — ^xy y. Idem fiat in z & pro- 
dibit a a z. Ponatur fumma faftorum aequalis ni- 
bilo, & habebitur sequatio 3 x x^ — x y y" — 'x y y 

'-j-a a z = o. Dico quod hac aequatione definitur re- 
latio fluxionum. 



[173] 
Demonftratio. 

Nam fit o quantitas admodum parva &: iunto 

0Z5 oy, ox, quantitatum z, y, x momenta id eft In- 
crementa momentanea fynchrona. Et fi quantita- 
tes fluentes jam iunt z, y & x, hae poft momentum 

temporis incrementis fuis oz, oy, ox auda?, evadent 

• • » 

z^-oz, y^-oy, x-j-ox, quae in aequatione prima pro 

z, y & X fcriptae dant aequationem x^ -l^^xxox 

^|- 3X00XX -j- 0^x3 — ^xyy — oxyy — ^xoyy — ^xooyy 

— xooyy-— -xo^yy -j-aaz-l-aaoz— b^ = o, Subducatur 

sequatio prior, & refiduum divifum per o erit ^xx^ 

-]- 3 xxox -j-^x^oo — xyy — ixyy -ixoyy — xoyy —xooyy 
-j-aaz^ o. Minuatur quantitas o in infinitum^Sc neg» 

le£tis terminis evanefcentibus reftabit gxx^-— xyy 

— ^xyy -f-aaz = o. Q. E, D. 

ExpUcatio plenion 

Ad eundem modum fi asquatio eflet xs— xyy 
4-aa f^ax — -yy—b^ =0, produceretur gx^x— xyy 
— 2xyy -^^aar'lax-— -yy — o. Ubi fi fluxionem/^ax — -yy 
tollere velis, pone //ax— yy = z, & erit ax— yy — z® 



[174] 

(per hanc Propofitionem ) ax-— -^yy^V.z feu 

^J- — z 5 hoc eft ■ JJ.^ = /^ax— yy , ht 

^z ^/^ax — -yy 

. . . a^x— laayy 

mae 3 x^x — xy y— 2xy y \ ^-— ' -- =0 

Vax— yy 

Et per operationem repetitam pergitur ad fluxio- 

nes iecundas, tertias & lequentes. Sit aequatio 

zy^"— z4-|-a4 = o, & fiet per operationem primam 

^y^^"'3^yy^"^42^^~o 5 perfecundam zy3-|-^6zyy2 
"\-3zyy2-|-6zy^y— 4.ZZ3— i^z2z^ = o , per tertiam 

-2y^-i- 9zyy' + 9zyy2 ^-. iSzy^y 4-.3zyy^^-^i8zyyy 

-|-^'6zy^"4.zz3— '5 6zzz2— 24.z^z ~ Oe 

llbi vero fie pergitiirad fluxiones fecundas, ter- 
tias & fequentes^ convenit quantitatem aliquam ut 
uniformiter fluentem con{iderare5& pro ejusfluxione 
prima unitatem fcribere^ pro fecunda vero & fe- 
quentibus nihil. Sit aequatio zy ^ — z"^ -]-; a4 — o, ut 
lupra; & fluat Ziiniformiter5fitq;.ejus fluxio unitas^ 

&fiet per operationem primam y^-]-^ 5 Zyy^—4.Z3 = 05 

per fecundam 6yy^ \i S^yy^ -^l- 6zy^y — - 1 2z^ = o, 

per tertiam 9yy'+i8y2y-]-^zyy^4.i8zyyy-1^6zy3 
—242 = 0. 

. In 



In hujus autem generis ^quationlbus concipieii- 
dum eft quod tluxiones in iingulis terminis fiat ejuf- 

dem ordinis, id eft vel omnes primi ordinis y^ z, 

vel omnes fecundi y, y^^ yz, z% vel omnes tertii 

y^ yy^ y^^ yS Th y^^ ^^ &<^'- Et ubi res aliter fe 
habet complendus eft ordo per fubintelleftas fluxio- 
nes quantitatis unlformiter fluentis. Sic aequatio 

Hoviffima complendo ordinem tertium fit 9Zyy^ 
+ ^^^Tl\V^lT\ ^ 8zyyy~^-.6zy3~i4.zz3 = o, 

PROP. IL PROB. IL 

Jnvenire Curvas qu^ quadrari fo^unt. 

Sit ABC figura invenienda, BC Ordinatim z^-Fig> ^. 
plica ta redangula^ & AB abfciffa. Producatur 
CB ad E ut fit BE—i^ & compleatur parallelo- 
grammum ABED: & arearum ABC, ABED 
fluxiones erunt ut BC & BE. Affumatur igitur 
sequatio quaevis qua relatio arearum definiatur^ & 
inde dabitur relatio ordinatarum BC & BE per 



Hujus rei exempla habentur in Propolitionibus 
duabus fequentibus. 



17^] 



PROP. III. THEOR. L 

Si pro abfclffa AB & area AE feu ABxi pro- 
miicuefcribaturZj&fipro e -[^ft!' ]-gz^'^ -{-hzh-^-Sac, 
fcribatur R : fit autem area Curvae zeR'^ erit, 
ordinatim applicata BC = 

^e t L fz' IJ gz'" IL hz3« -H &c. in z ^-^ R ^-^ 



Demonftratio. 

Nam fi fit z^R^^v, erit per Prop, i, ^zz^-'R;^ 

« • « 

'^-AZ^RR'^'^ = V. Pro Ra in primo sequationis ter- 
mino & z® in fecundo fcribe RR^"^ & zz^"^, & fiet 

szR -|- azR in z®'' R^^ = v, Erat autem R = e -|- f z» 

-l-gz^«^[-hz3« &c. & inde per Prop. i. fit R =; 

?3fzz«"V-[-2Hgzz^»'\4^iMhzz3«-^^j- &c. quibus fubftitu- 

tis & fcripta BE feu i pro z, fiet 
»e.mfzi|^^gz^»:|:«^hz3»4.&c. in z8-R^- = v=BC. 

Cjt» E. De 



PROP. 



1^71 1 



PROP. IV. THEOR, 11. 



Si Curvae abfciffa A B fit z, & fi pro q\- f z" -)-gz'« 
-]-&c. fcribatur R, & pro k-4"lz«-j~^mz^"-|- &c. fcri- 
batur S ; fit autem area Curva? z^ R^ S^ : erit or- 
dinatim applicata B C == , 

9ek~!^ f k z" i^ gkz^'* ' ^ * i 

M-XM H-2AMD B 



glz3» * 



2A„ 5^^ ^ i^ z^-'R^-'S«*"' 



-AM '1-2AM 

Demonftratur ad modum Propofitionis fiiperioris. 

PROP. V. THEOR. IIL 

Si Curv^ abfcifla AB fit z, & pro e-j-fz^'-l-gz^" 
■^-hz^" -Y &c. fcribatur R : fit autem ordinatim ap- 
plicata z^-'R'^'' in a -|-bz" ^l-cz^" -l-dz3«-i- &c, & po- 

natur J-r. r-j-^^s. s-j-'^^t. t-l-A==v<&c. erit area 

re r-h I ,e M^T, e r^+lje 

-^- -- -^^ ^^ z4« ~1- &c. Ubi A, B, C, D, &c. 

r-t-4, e 

Aaa denotant 



[178] 

denotant totas coefficieiites datas termlnorum (ingu- 
lorum in ferie cum fignis fuls-|-& — ^nempe A primi 

termini coefficientem ^ B fecundi coefficientem 



i-e°) 



^b~sfA r>. .- rr • .7cZ;fB— tgA ^ 

"._-____, C terhi ropfRriPnl-pm " ^ , & 

r -H- I , e r — h 2, e 

fic deinceps. 

Demonjiratio. 
Sunto juxta Propofitionem tertiam^ 

Curvarum Ordinatae & earundem areas. 

I . eeA tlf Az" tLg Az^« '\l h Az^^'Sc c. 1 ' Az^ R^ , 



s etii, eBz" t®-i"«f B z^" t^-UgBzS" &c. I Bze-h" R\ 

3 ' - • ' +9T^,eCz'«:p-l-2«fCz3^ &c. 



^ z^-iRvi, 



Cz9-NhR\ 



+9-'h«5eDz3"&c.j Dz^-'^3« R^ 



Et fi fumma ordinatarum ponatur ^qualis ordi- 
natae a^|-bz"'|-cz^^~dz3"-|- &c. in z^-'R^-', fumma 
arearum z^R^ in A~j-Bz"'pCz^"-j-Dz3"-|- &c. sequa- 
liseritare^ Curves cujus ifta eft ordinata. ^quen- 
tur igitur Ordinatarum termini correipondentes, & 
fiet a-eeA, b = .i_«„fA:l^eB, c= .y^^t^' fB 

.^j- 0-l-2„5eC 6CC. & mde g^ =^ A. 



C~[9-1-2A„. gA-;9-i-r!-A«,fB ^ T- r 1 • 

-~- — — Q_|_2„, e ~— =: i^. jit lie demceps m mfi 



3S i 

nitum 



C 179 } 

iiitiim. Pone jamS-r. r-j-A^^s. s-J^x^t &c. & 

in area z^R^x A-VBz"^J-Cz^"-|-"Dz3» &c. fcribe ip 
forum A^ B, C, &c. valores inventos & prodibit 
feries propofita. Q. E. D. 

Et notandum eft quod Ordinata omnis duobus 
modis iu feriem reiblvitur. Nam index "vel afEr- 
mativus eft poteft vel negativus. Prpponatur Ordi- 

nata ----^^ -p-^- — ^, Haec vel fie fcribi poteft 

z-ix 5 k— Izzxk — IzzA-mz^j'^^ vel fie zx-l-j-^kF^ 
xm-lz""'-l-kz"~^, -i. In cafu priore eft a— ^Eb^o. 

C=— 1. e==k. frrrO. g= J. h=m. ^^=—1. n=:I, 
9-1=-^. ^=-l=l\ S=-I. t=--^. Vrr=0. In 

pofteriore eft a = — 1. b=o. c^^k. e=m. f==— 1. 

g=0. h^=I. ^=—1 ^i=—l. Q— 1:^1. 0=2. r=— 2, 

s=— i^. t=— I. v=— '. Tentandus eft cafus uter- 
que. Et fi ferierum aiterutra ob terminos tandem 
deficientes abrumpitur ac terminatur, habebitur area 
Curvae in terminis finitis. Sic in exempli hujus 
priore cafu fcribendo in ferie valores ipforum a, b^ 
c, e, f, g, h, A, 9, r, s^ t, v, termini omnes poft pri- 
mum evanefcunt in infinitum Sz. area Curra prodit 

— ■2V^ '~z3^ '''^\ Et ha?c area ob fignum negativum 
adjacet abfciffe ultra ordinatam produd^. Nam 
area omnis affirmativa adjacet tarn abfciife quam 
ordinate, negativa vero cadit ad contrarias par- 
tes ordinatae & adjacet abfcilfe produdse^ manente 
fcilicet figno Ordinatce. Hoc modo feries aiter- 
utra & nonnunquam utraque fem^per termlnatur 
& finita evadit fi Curva geometrice quadrari po- 
teft. At fi Curva talem quadraturam non admit- 
tit, feries utraq; continuabitur in infinitum^ & ea- 

A a a 2 



[i8o] 

rum altera converget 8c areamdabit approximandoy 
praeterquam ubi r ( propter aream infinitam ) vel 
nihil eft vel Humerus integer & negativus, vel ubi ^ 
iiequalis eft unitati. Si '^ minor eft unitate, conver- 
get feries in qua index „ affirmativus eft : fin I unita 

te major eft, converget feries altera. In uno cafii 
area adjacet abfcilTas ad ufq; ordinatam dufta?, in 
altero adjacet ablciffas ultra ordinatam produilo?. 

Nota infuper quod ii Ordinata contentum eft fub 
feftore rationali Q & fadore furdo irreducibili R'^^ 
& faftoris furdi latus R non dividit factorem ratio- 
nalem Qj erit a-i =t & R'^'^ - R'^. Sin factoris fur- 
di latus R dividit faftorem rationalem femel, erit 
A-»i=r=7r-|- I & R^'^ r=z=R''+^ \ ft divldlt bls , erit 
A=-i=r=r7r^|-ci & R^^'^ =:R'^-1"^: fi ter, erit a-i^tt-J^^^, 
& R^-^=:R''-»'3 : & ficdeinceps. 

Si Ordinata eft fradio rationalis irreducibilis cum 
Denominatore ex duobus vel pluribus terminis com- 
pofito : refolvendus eft denominator in divifores 
faos omnes primes. Et fi divifor fit aliquis cui 
iiullus alius eft sequalis , Curva quadrari nequit : 
Sin duo vel plures lint divifores sequales, rejicien- 
dus eft eorum unus, & fi adhuc alii duo vel plures 
fint fibi mutuo ^quales & prioribus ina^quales, re- 
jiciendus eft etiam eorum unus, & fie in aliis omni- 
bus aequalibus fi adhuc plures fint : deinde divifor 
qui relinquitur vel contentum fub diviibribus omni- 
bus qui relinquuntur, fi plures funt, ponendum eft 
pro R, & ejus quadrati reciprocum R'^ pro R'^'^^prse- 
terquam ubi contentum illud eft quadratum vel cu- 
bus vel quadrato quadratum^&c. quo cafu ejus latus 

ponen- 



[i8i] 

ponendum eft pro R & poteftatis index 2 vel 3 vel 4 
negative fumptus pro a. & Ordinata ad deiio'iiina^ 
torem R^ vel R^ vel R^ vel R^ &c. reduceoda. 

lit ft ordinata fit ^^l±^4=:i23 . anoni'^m li-r 

fraftio irreducibilis eft & denominatoris divi fores 
funt pares.^^ nempe z— i, z— i, z— i & z-]-a, 
Z'j-i, rejicm magnitudinis utriufque diviforem 
unum & reliquomm z— i, z — i , z-|-2 content 
turn z^ — ^3^-1-^ pono pro R & ejus quadra ti re- 
ciprccum "^^ feu R~2 p^.Q ^k-^i j^^^^ Ordina> 

tarn ad denominatorem R^ feu'R'-^reduco, & fit 

z^- 9z^-l-8z3 ______ ■ 

Et inde eft a = 8, b=-9. c = o. d^=-i^ &c 
e=a. f=~^, g = o. h==i. ^-i=r-.2. ;,~_K 

„— I. 9-1 — ^. 9=r4=:r. S— 3. t==:2. V=I. Et Ills 

in ferie fcriptis prodit area -11-— ^ terminis om- 
nibus in tota ferie poft primuin evanefcentibus. 

Si deniq; Ordinata eft fraffio irreducibilis & ejus 
denominator contentum eft fob fadore rationali Q 
& faftore furdo irreducibili R'^, inveniendi funt la- 
teris R diviforcs omnes primi«, & rejiciendus eft di- 
vifor unus magnitudinis cujufq; & per divifores 
qui reftant , fiqui fint , multiplicandus eft fa£tor 
rationalis Q : & fi fadum a^quale eft lateri R vel 
lateris illius poteftati alicui cujus index eft numerus 
integer, efto index ille m^^ & erit a— i ^— ^— m, &. 

R^--R— . UtfiOrdinatafit-^^-^^ "^-^^-^"-^^"-^^^^% 

quonj'am. 



.[182] 

quoniamfaftoris fiirdi latusR feu q3-]-qqx-qxx-X5 
diviibres habet q-1 X5 q^-x, q— xqui duarumfunt 
magiiitudinuin, rejicio diviforem uiium magnitudi- 
nis utriufq; Sc per diviforem q-j-x qui relinquitur 
multiplico faCtorem rationalem qq — xx. Et quo- 
niam faftum q^-j-qqx — qxx — x^ ^quale eft la- 
teri R^pono m=i. & inde^ cum tt fit |, fit ^-^i =-.^. 
Ordinatam igitur reduce ad denominatorem R:l 

& fit Z°x 3qM-^q^x+8q^xx-l-8q^x^~7qqx'~6qx^ 
X q5 -j- qqx — qxx— xl^^^-.Unde eft a — 5 q^ b = iq^ &c. 
e-qs. f-qq&c. 9 — 1=^0. 0=1— «. ;, = — ■. r= i. 
tr='. v:=o. Et his in ferie fcriptis prodit 



2 



area . ^ , , — - ^ termmis ommbus m ferie tota 

^cub. a3-l-aax — axx — x^ ^ 

poft tertium evanefcentibus. 



PROP. VI. THE OR. IV. 

Si Curvae abfciffa AB fit z, & fcribantur R pro 

e^-fz« -|-gz^« -|-'hz3»-l-&c. & S pro k "l-lz« -l-mz^^ 
"j-nz^" &c. fit autem ordinatim applicata z^-'R^"^ S^-' 
in a-|-bz« -j-cz^" --\-dz3" &c. 8c fi terminorum, e^ f, 
gj \ &c. & k, I5 m^ n. &c. reftangula fint. 

ek fk gk hk &c. 

el fl gl hi &c. 

em fm gm hm&c. 

en fn gu hn &c. 

Et 



Et fi reSanguloriim illorum coefficieiites nume- 
rales fint refpeftive 



«"9 = r. Y-\-y\^S. S-|-A-t. t-'p^=V. &C.' 

. S-j-/,— t. t-|-^==V. V-\--"^W. W'j-/"=X. &c. 

area Curvae erit h^c 

'-— 1 2 k 
- q -h — 5 ^^ A ' r —5^-17 f k D — t' f 1 A 

6D>C • " «^_3,ei^ hC-.s'4i el J^-t"enA 

z^R^S/^m - — ^ j_ — -^ ,rJ--^-~^ — — , 72«. 

rek 1 r-|-i,ek ' fTT,ek ^ 

___ __v hkA ' - 

___ -t-)-i,gk^_v'gl^ 

Lj ~s-1-2, fkp — t'-l-i,fl -D _v"fm 
« <^ — s'-l-2, e l"^ -t'Vi-i,e m _v'"e n 



,z5« M-, Sec. 



r-i-3»ek 



Ubi A denotat termini primi coefficientem datani 

»L^ cum figno fuo ■\^ vel — , B coefficientem datam 

fecundi, C coefficientem datam tertii^Sc fie deinceps. 
Terminorum vero^ a^ b, c, &c. k, 1, m, &c. unus 
vel plures deeffe poffunt. Demonftratur Propofitio 
ad modum prsecedentis, & qu-^ ibi notantur hie ob- 
tinent. Pergit autem feries talium Propcfitionum in 
infinitum^ &Progreffio feriei.manifefta eft. 



PROP. 



liHl 



PROP. VII. THEOR, V. 

Si pro e 4-fz"-|-gz^«4- &c. fcribatur R ut fupra, & 
in Curvs alicujus Ordinata z^inor'R_K±T maneant 
quantitates datae 0, h, a^ e, £> g, &c. & pro ^ ac t fcri- 
bantur fucceflive numeri quicuiiq; integri : & fi 
detur area unius ex Curvis quos per Ordinatas in- 
niimeras (ic prodeuntes defignantur fi Ordinatoe funt 
duorum nominum in vinculo radicis^ vel fi dentur 
areoe duarum ex Curvis fi Ordinatoe lunt trium no- 
ininum in vinculo radicis, vel area: trium ex Curvis 
fi Ordinatoe funt quatuor nominum in vinculo radi- 
cis, & fie deinceps in infinitum : dico quod dabun- 
tur areoe curvarum omnium. Pro nominibus hie 
liabeo terminos gmnes in vinculo radicis tarn de- 
ficientes quam plenos quorum indices dignitatum 
funt in progreffione arithmetica. Sic ordinata 
Va^ — ax3 -j- x^ ob terminos duos inter a*& — ax^ 
deficientes pro quinquinomio haberi debet. At 

Va'^-i-X4 binomium eft & V^'^-J-^x^ — ^ trinonium^ 
cum progrelTio jam per majores differentias proce- 
dat. Propofitio vero fie demonftratur, 

Sunto Curvarum duarum Ordinatoe pz®'^ R'^-' & 
qzM«-iR_A-i^ & areoe p A & qB, exiftente R quanti- 
tate trium nominum e-j~fz«'j-gz'«. Et cum per 

Prop, 



Prop. III. fit z^R^ area curvae cujus Ordinata eft 
fle:|:^/z«:jN ^gz^« in z«-R-^,fubduc Ordinatas & areas 
priores de area & Ordinata pofteriori, & manebit 
% 11/^V|l« g^'"^« ^"''^"' Ordinata nova Curv^,& 

— qz" 

z^R'^ — pA— ^qB ejufdem area. Pone se-p & 
df-j-Awf rr=q & Ordinata evadet J 2z^» in z^-'R'^'L & 
area z'R'^ — eeA — efB — A»fB. Divide utramq; per 
9g-|-.^A«g^ & aream prodeuntem die C, & afliimpta 
utcunq; r, erit r C area Cuvvx cujus Ordinata eft 
i-zfl-Htf-iR^-i, Y.t qua ratione ex areis pA & qB 
aream rC Ordinata? rz^'l"^«'^ R^"' congruentem inve- 
nimus, licebit ex areis qB & rC aream quartam 
puta sD, ordinatae sz^+^n |{^a-i congruentem invenire, 
& fic deinceps in infinitum. Et par eft ratio pro- 
greflionis ab areis B & A in partem contrariam 
pergentis. Si terminorum 95 9-|-'^»,& 9-^-2a„ aliquis de- 
ficit & feriem abrumpit^ allumatur area pA in prin- 
cipio progreffionis unius & area qB in principio a.U 
terius, & ex his duabus areis dabuntur areae omnes 
in progreffione utraque. Et contra, ex aliis duabus 
areis alTumptis fit regreffus per analyfin ad areas A 
& B, adeo ut ex duabus datis caeterae omnes den- 
tur. Q. E. O. Hie eft cafus Curvarum ubi ipfius z 
index G augetur vel diminuitur perpetua additione vel 
fubdudione quantitatis **. Cafus alter eft Curva*^ 
rum ubi index ^ augetur vel diminuitur unitatibuso 



■L ji S» 



[i8d3 



C jl S. IL 

Ordinatse pz^'^R^ & qz^+^-'R'^, quibus areae pA 
& qB jam refpondeant, fi in R<feu e-j-fz^ + gz^" du- 
cantur ac deinde ad R viciffim applicentur, eva- 
dunt pe -\- pfz^ -\- pgz^" x z^-'R'^"^ & qez'' -j- qfz^*^ 
J-qgz3« X z^-^R^-'. Et per Prop. HI. eft az^R^^ 
area Curvae cujus Ordinata eft sae :j:J^afz\|^^^agz^*' 
in z^-^R^"^ 5 & bz^'^'^R^ area Curvae cujus ordinata 
eft .|-5bez« tjbfz^" t-J^gz^" in z®-'R'^-^ Et harum qua- 

tuor arearum fumma eft pA-|-qB'|"' az^R'^-j-bz^'l'^R^ 
& fumma refpondentium ordinatarum 

^ae t® afz« tl asz^« V bgz^" in z^-^R^^-^ 
. ^ f be f bf ^ 

+ pf 

+ qe + qf 

Si terminus primus tertius & quartus ponantur fe- 
orfim aequales nitiilo, per primum fiet 0ae^i-pe = o 
feu --«a = p5 per quartum — 9b — »b — 2 Awb = q ^ & per 

tertium (eliminando p & q) t = b. Unde fecundus 

fit ^^-7^^^^, adeoq; fumma quatuor Ordinatarum eft 

^^^'z^'^'«'^R^-S& fumma totidem refpondentium 

arearum eft azSR^^^ip^s+^R^^eaA— '-^^^^^ 

Divi- 



C 187 ] ^^ 

Dividantur hse fummas per ^. — r^*'^ & fi Quotum 
pofterius dicatur D, erit D area curvge cujus ordi- 
nata eft Quotum prius z^+^'^R^'^ Et eadem ratione 
ponendo omnes Ordinatae terminos praeter primum 
aequales nihilo poteft area Curvas inveniri cujus Or- 
dinata eft z^'^R^'^ Dicatur area ifta C, & qua ra- 
tione ex areis A & B inventas funt areae C ac D, ex 
his areis C ac D inveniri poffunt aliae duae E & F 
ordinatis z^'^R^'^ & z^-V^^^R^-^ congruentes, & fie de- 
inceps in infinitum. Et per analyfin contrariam 
regredi f licet ab areis E&Fad areas CacD, & 
inde ad areas A & B, aliafq; quae in progreflione fe- 
quuntur. Igitur fi index ^ perpetua unitatum ad- 
ditione vel liibduftione augeatur vel minuatur, & 
ex areis quae Ordinatis fie prodeuntibus refpondent 
duae fimpliciflimae habentur j dantur aliae om_nes in 
infinitum. Q, E, O. 



C ^ S. Ill 

Et per cafus hofce duos conjunftos, fi tarn in- 
dex e perpetua additione vel fubdudione ipfius^^ 
quam index x perpetua additione vel fubduCtione 
unitatis, utcunq; augeatur vel minuatur, dabuntur 
areae fingulis prodeuntibus Ordinatis refpondentes, 
Q. E. O. 



Bbbi CJtS. 



[i88] 

C A S^ IV. 

Et fiinili augmento fi ordinata conftat ex qua- 
tuor nominibus in vinculo radicali &: dantur tres 
arearum, vel fi conftat ex quinq; nominibus & 
dantur quatuor arearum, & fie deinceps : dabun- 
tur areoe omnes c\nx addendo vel fubducendo nume- 
rum n indici 6 vel unitatem indici x generari poffunt. 
Et par eft ratio Curvarum ubi ordinatae ex binomiis 
conflantur, & area una earum quos non font geome- 
trice quadrabiles datur. Q. E. O. 

PROP. VIII. THEOR. VL 

Si pro e4-fz"-l-gz^«'|-&c. & k + Iz" -l-mz^-|-&e. 
fcribantur R & S ut fopra,& in Curvoe alicujus Or- 
dinata z®+"'' R^l^ S^^l ** maneant quantitates datae e, 
M, A, F, e, f, g, k, 1, m, &c. & pro ^^^ t, & v^ fcri- 
bantur fucceffive numeri quicunq; integri : & fi 
dentur area? duarum ex curvis quae per ordinatas 
fie prodeuntes defignantur fi quantitates R.& S font 
binomia, vel fi dentur arese trium ex. curvis fi R 
& S conjunftim ex quinq; nominibus conftant, vel 
areae quatuor ex curvis fi R &S conjundim ex fex 
nominibus conftant, & fie deinceps in infinitum : 
dico quod dabuntur areae curvarum omnium. 

Demonftratur ad modum Propofitionis fiiperioris. 

PROP. 



[i89] 



PROP. IX. THE OR. VIL 

^quantur Curvarum arese inter fe quarum Or- 
dinate funt reciproce ut fluxiones Abfciflarum.^ 

Nam contenta fub Ordinatis & fluxionibus Ab- 
fciflarum erunt asqualia^ & fluxiones arearum funt 
ut hgec contenta. 

COROL. L 

Si aiTumatur relatio qusevis inter Abfciffas dua^ 
rum Curvarum, & inde per Prop. i. quseratur 
relatio fluxionum Abfciflarum, & ponantur Ordi^ 
natae reciproce proportionates fluxionibus, inveniri 
poflRmt innumerae Curvas quarum areas fibi mutuo 
aequales erunt. 

COROL. IL 

Sic enim Curva omnis cujus haec eft Ordinata 
z^' in e -y- fz^-^gz^" -[- &C.1'' affumendo quantitatem 
quamvis pro r & ponendo ^--s Sc z^^x, migrat in 
aliam fibi aequalem cujus ordinata eft =x— ^ in 

^fx^_+gx^^4.&c;|^« 



1 19^ ] 
COR.OL^ III. 

Et Curva omnis cu jiis Ordinata e ft z^'' in 
a"^bz«~^Pci2^&c". X e-i-fz«'i-gz^« &c.Kaffumen- 
do quantitatem quamvis pro »' & ponendo J.= s & 
z^^x, migrat in aliam fibi oequalem cujus ordinata 

eft V-^ in a+bx''+cx^''-t&c."xe4-fx''J-gx^^'i-&c.^ 

COROL. IV. 

Et C urva omnis cu jus Ordinata eft z^" in 
r+rbz""'!- c z"» + Sec . X e -(- fz« i- gz^" -i- Sec. j^ 
xk 4- Iz" -b mz^» -r Scc.^ affumendo quantitatem 
quamvis pro v & ponendo l-=s & z^ = x, migrat in 
aliam fibiaequalem cujus ordinata eft ^x'i=-" in a-p bxi^ 

COROL, V. 

Et Curva omnis cujus Ordinata eft z^'^ in 
eTuf^>ripp^irip&^j^ ponendo i= x migrat in 

aliam fibi ^qualem cujus ordinata eft ^^ x^'V'^^'' 

»--»—,, . , n. —^ v/f J-.ex«h fiduo funt 

'T"^-2« ^ ^c> id eft xH-^-l-«^^ .^ - ^1 

nomina in vinculo radicis vel -^p^K x g+f^M' 
fi tria funt nomina ; & fie deinceps. 



ex^"l 



CO- 



[ 191 ] 

COROL. VI. 

Et Curva omnis cujus Ordinata eft z^"' in 

e -\-{z»-\- gz^-P SccJ'^ X k -|- lz« -|- mz^"-)- &c.[f^ 

ponendo J — x migrat in aliam fibi aequalem cu^ 

jus ordinata eft ~^p, x e -|- f x-" ^|- gx"^" -|- *^c^|^ 

X ' 

xk+lx-« +mx--«| &c|^ id eft ^q,!.;.,-,,.;,,^ x f+exf 
xl-i kx^i'^ fi bina funt nomina in vincuHs radicum, 
vel x^T-i-F^iM^ii^ X g -j- fx" -|- ex^wp x l-|-kx«p fi tria 

funt nomina in vinculo radicis prioris ac duo in 
vinculo pofterioris : & fie in aliis. Et nota quod 
areae duse aequales in noviffimis hifce duobus Co- 
roUariis jacent ad contrarias partes ordinatarum. 
Si area in alterutra curva adjacet abfcilTce , area 
huic aequalis in altera curva adjacet abfciflb pro» 
dud:a\ 

COROL. VIL 

Si relatio inter Curvae alicujus Ordinatam y & 
Abfciffam z definiatur per aequationem quamvis 
feftam hujus formse^y « in e ~|- fyz^-j-gy^wz^^-f- hy3«z^^ 
+ &c. = z^ in k -i" ly"zJ^ -j- my ^^z"^ -|- &c. ha^c 
figuraaffumendos-:2=i, x-^l^^' 8cx=^;^^^ migrat 
m aliam fibi aequalem cujus AbfcifTa x/ex data 

Ordinata 



[^92] 

Ordinata v, determinatur per a^quation em non 

^i-mv'"-l-&c.r:=x. 

COROL, VIII. 

Si relatio inter Curvss alicujus Ordinatam y & 
Abfciffam z definitur per aequationem quamvis 
atfeitam hujiis format, y* in Q\--iyz^'-\-gy'^'^ z^^ -H&c 
==z^ in k^^'\Yz^^my^''^'^\^. +z>' in p^-qy V 
j.y2M22dr^j_ ^j^ggc figuj;^ afluniendo s- ^,x= '-z^^ 



M^^^'Sc ^ = ^— J, migrat in aliam fibi asqualem 
cujus Abfciffa x ex data Ordinata v determinatur 
per aequationem minus afFeftam v* in e -j- fyw-l-gv^"* 

-\- &c. = s'^x'^ in k 4- lv« -\- mv^'' ^-^ &c. -Y s'x' in 



CO ROL. IX. 

Curva omnis cujus Ordinata^ eft tz^'' in 



(a -1- b \qz' + fzH-H -1 - gz^t« ._|- &c.lf ^ fi fit 9 ^ 'x & 



<r-t 



affamantur x-ez" 4:^fz-l-« +gz''+^»^-&c.h , 
& -^ =^ in, migrat in aliam fibi sequalem cujus ordi- 
nata eft x*^^ xa-j bx'^j *'. Et nota quod ordinata prior 

in 



t 



[193]. 

in hoc CoroUario evadit fimplicior ponendo k 
vel ponendo ^ = i & efficiendo ut radix dignitatis 
extrahi poffit cujus index eft «, vel etiam ponendo 
«»=— i&^ = i=T = '^—TTj ut alios cafus praete- 
ream. 

COR.OL. X. 

Pro ez»' 4- fz'-i-^ -|- gz'-^-^» -|- &c. ^qz'-' :}:;;fz^^''*-' 

T2 gz"'^'"^"'' -V ^^- '^ V ^^^ "i' ^^""^ '1'^ ^^- ^ "^^""^ 
,-^ inmz^"-' 4'^^' fcribantur R, r, S & s refpeftive, & 
Curva omnis cujus ordinata eft TrSr -^ p Rs in R'^-' S<*"' 
X aS^4-bR^ , ft fitiJiziii* = '^ = 5 i =r cr ^-'f = ^ 

& R*S9 = x, migrat in aliam fibi aequalem cujus or- 
dinata eft x^ X a^pbPp. Et nota quod Ordinata 
prior evadit fimplicior^ ponendo unitates pro t, v^ 
& ^ vel i*.^ & faciendo ut radix dignitatis extrahi 
poffit cujus index eft «, vel ponendo « — r-i vel 

PROP. X. PROB. IIL 

Invenire figuras fimpliciffimas cum quibus Curva 
qucEvis geometrice compari poteft, cujus ordinatim 
applicata y per sequationem non affe6tam ex data ab- 
fcifla z determinatur. 



C c c 



[194] 

C A S. I. 

Sit Ordinata az^-\ & area erit iaz\ ut ex Prop.V. 
ponendob^o = c = d = f^g=h Sce^i, facile col- 

ligitur. 

C AS, 11. 

Sit Ordinata az^-^ x^e^j-^fz^^- gz^f^'' -]- &c. & fi 
curva cum figuris reftilineis geometrice comparari 
poteft, quadrabitur per Prop. V. ponendo b = o-c 
c=d. Sin minus convertetur in aliam curvam fibi 



K'l 



aqualem cujus Ordinata eft -„x^ x e-j-fx-j-gx^&c. 
per Corol. a. Prop. IX. Deinde fi de dignitatum 
indicibus ^ g^ ^-i per Prop. VIL rejiciantur uni- 
tates donee dignitates ilk fiant quam minima, de- 
venietur ad figuras fimpliciffimas qux hac ratione 
colligi poffunt. Dein harum unaqua^q; per Corol. 5. 
Prop. IX. dat aliam quae nonnunquam fimplicior 
eft, Et ex his per Prop. III. & Corol. 9 & lo^ 
Prop. IX. inter le coUatis, figura: adhuc (impliciores 
quandoq; prodeunt. Deniq; ex figuris fimplicif- 
fimis ajGTumptis fafto regreffu computabitur area 
qusefita. 



CAS. 



[195 3 

C A S. III. 



Sit Ordinata z^'' x a -^^ bz« -j- cz^« 4-- &c. 

X e -\-' fz" -I" gz^" 4^ &c.l^"' , & haec figura fi quadrari 
poteftj quadrabitur per Prop. V. Sin minus, di- 
ftinguenda eft ordinata in partes z^-' x a x e -j- f z« 

+ gz^" -1- 8cc.l^-^, z®-^ X bz« X e^- f z« +-g z^«-|-&c.H, 
&c. & per Caf. 2. inveniendae funt figurae fimpli- 
ciffimse cum quibus figurse partibus illis refpon- 
dentes comparari poflunt. Nam areae figurarum 
partibus illis refpondentium lub fignis fuis -j- & — 
conjunfitae component aream totam qusefitam. 

CAS. IV. 



Sit Ordinata z^'^ x a -(- bz^J-Hcz^" +&c x 
e-j-^ fz» -j- gz2« -|- &C.H X k -[- Iz» -^mz^«i-&c.|t^-f: 
& fi Curva quadrari poreft^quadrabitur per Prop. Vt 
Sin minus, convertetur in fimpliciorem per Corol.4. 
Prop. IX. ac deinde comparabitur cum figuris fim- 
pliciffimis per Prop. VIII. & Corol. 6, 9 & 10. 
Prop. IX. ut tit in Cafu 2 & 5. 

C A S, V, 

Si Ordinata ex variis partibus conftat 5 partes 
fingulse pro ordinatis curvarum totidem habendae 
funt5& curvae illae quotquot quadrari poffunt^figilla- 

Ccc a tim 



tim quadrandae funt, earumq; ordinatae de ordinata 
tota demendae. Dein Curva quam ordinatos pars 
refidua defignat feorfim ( ut in Cafu i^ 3 & 4.5) 
cum figuris iimpliciffimis comparanda eft cum qui- 
bus comparari poteft. Et fumma arearum omnium 
pro area Curvss propofite habenda eft< 

COROL. I. 



Mine etiam Curva .omnis cujus Ordinata eft ra- 
dix quadratica affe£i:a oequationis fuoe, cum figuris 
fimpliciffimis feu redilineis leu curvilineis com- 
pari poteft. Nam radix ilia ex duabus partibus 
lemper conftat quae feorfim fpectat^ non fant aequa- 
num radices affeftas. Proponatur aequatio aayy 
-]- zzyy — ^a'y -|-'z3y — z% & extra£la radix erit 

_ a^ -\- z^^ aVa^-l-'^z^— z* cujus pars rationalis 



aa - - zz 



ar-Vz:? ^ . . -. aVa^ -1^ laz^^ - z'' 

aa-^-zz & pars irrationalis ^^r^ii ~ l^fit 

ordinatas curvarum quae per banc Propofitionem 
vel quadrari poffunt vel cum figuris fimpliciffimis 
comparari cum quibus coUationem geometricam ad- 
mittunt. 



VOROL. IL 



Et curva omnis cujus Ordinata per aequationem 
quamvis affeftam definitur quae per Corol. 7. Prop. 
IX. in aequationem non affeftam migrat, vel qua- 

dratur 



[ 197 ] 

dratur per hanc Propofitionem li quadrari poteft vel 
comparatur cum figuris limpliciffimis cum quibus 
compari poteft. Et hac ratione Curva omnis quadra- 
tur cujus aequatio eft trium terminorum. Nam squa- 
tio ilia ft affedta fit tranfmutatur in non afFedam per 
Corol.y. Prop.IX. ac delude per Corol. ^ & 5. Prop. 
IX. in fimplicflimam migrando^ dat vel quadratu- 
ram figurae fi quadrari poteft, vel curvam fimplicif- 
fimam quacum comparatur. 

COROL. III. 

Et Curva omnis cujus Ordinata per isquationem 
quamvis affedam definitur qucE per Corol. 8. Prop. 
IX. in aequationem quadraticam aiFedam migrat; 
vel quadratur per hanc Propofitionem & hujus Co- 
rol. I . fi quadrari poteft, vel comparatur cum figu- 
ris fimpliciflimis cum quibus coUationem geometric 
camadmittit. 

SCHOLIUM. 

Uti quadrandas funt figurae; ad Regulas hafce 
generales femper recurrere nimis moleftum effet : 
prseftat Figuras quae fimpliciores funt & magis ufui 
effe poflfunt femel quadrare & quadraturas in Ta- 
bulam referre, deinde Tabulam confulere quoties 
ejufmodi Curvam aliquam quadrare oportet. Hu- 
jus autem generis funt Tabulae duae fequentes, in 
quibus z denotat Abfciffam, y Ordinatam redan- 

gulam 



[198] 

gulam & t Aream Curvse quadrandae, & d,, e, f, g, 
g. h, " funt quantitates datae cum fignis fuis-|-'&— . 

TABULA 

Curvarumjimpliciorum qu^ quadrari pojfmt. 

Curvarum formge. Curvarum areae. 
Forma prima. 
dz«-' = y, -z" = t. 

Forma fecunda. 
dz*^' dzn — d ^^ 

Forma tertia. 



i.dz,iVe^|-'fz« = y. |;fR^^ = t, exiftente R^V^-j-^fz" 

a. dz!?\/e-l-fz*'=^y. °~" i5«ff " dR^ —t. 

, „ / — —-r — i6ee— .24efzM-|-3offz2M ,^ 

3 . dz?« Ve 'l-fz« = y . ^^^ — dR^ =. t. 

1 ^« /"^Tr^ ^96e3-\-i44eefzn— i8oeffz2H-l-2iof323 ,),.^ 

4. dzljVe-i-tz*'==y. -^ ^:;^r- ^dR^^t. 

Forma quarta. 

dz»'i 2d 

;^€^-fZtj 

dz^«- 



^. =y- :=l|^dR-t. 



dz3«^ 



Ay^n-i J6ee-~8efz„-|-6ffz2„ 

(|2i4ri — 96e3-|-4Seefz>r-36effz2,rl-3of3Z3,) 



TABULA 

Curvarum Jhnpliciwum qua cum EUi^ S 
Hyperbola compart pojfmt. 



>3 



Sit jam aGD vel PGD vel GDS Seaio 
Conica cujus area ad Quadraturam Curvse pro- ^^g* 5?<^s7>S. 
pofitae requiritur, fitq; ejus centrum A, Axis K a, 
Vertex a, Semiaxis conjugatus AP^ datum Abfciffe 
principium A vel a vel a^ AbfcilTa AB vel a B vel 
aB^^x^ Ordinata reftangula BD = v, & Area 
A B DP vel aBDG vel aBDG = s, exiftente ^G Or- 
dinata ad punftum «. Jungantur KD, AD, aD. Du- 
catur Tangens DT occurrens Abfciflfe AB in T, 
& compleatur parallelogrammum ABDO. Et 
fiquando ad quadraturam Curvge propofitse requi- 
runtur arese duarum Sedionem Conicarum, dica- 
tur pofterioris AbfcilTa?, Ordinata T^ & Area o-. 
Sit autem ^ differentia duarum quantitatum ubi in- 
certum eft utrum pofterior de priori an prior de po- 
fteriori fubduci debeat, 

Curva- 



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[205] 

In Tabulis hifcc, feries Curvarum cujufq; formae, 
utrinq; in infinitum continuari poteft. Scilicet 
in Tabula prima, in numeratoribus arearum for- 
mx tertise & quarts, numeri coefficientes initialium 
terminorum (1, — +«,i6, — ^96, 868^&c.) generan- 
tuT multiplicando numeros^ — 2, — ^^ — 6, —10 &c« 
in fe continuo, & fubfequentium terminorum coef- 
ficientes ex initialibus derivantur multiplicando 
ipfos gradatim, in Forma quidem tertia , per — '- 
—h—ly—h —To &<^'- in quarta vero per — I, _i'' 
—h — h — h &c. Et Denominatorum coefficientes 
5, 15, 105, &c. prodeunt multiplicando numeros 
I5 5, 5, 7, 9, &c. infe continuo. 

In fecunda vero Tabula, feries Curvarum fornix 
prim^, fecundae, quintae, fextae, nonae & decim^ ope 
folius divifionis, & formae reliqus ope Propofitio- 
nis tertiiB & quartae, utrinq; producuntur in in- 
finitum. 

Quinetiam has feries mutando fignum numeri ^^ 
variari folent. Sic enim, e. g. Curva |\/e+fz«~ y 
evadit -r--- yf-V-ezw, 

P R O P. IX. T H E O R. VIIL 

fSit A Die Curva quavis Abfciflam habens 
AB=z & Ordinatam BD=y, & fitAEKC Curva 
alia cujus Ordinata BE squalls eft prions ares 

ABC 



?• 



[20(J] 

ADB ad unitatem applicat-3e^ &AFLC Curva 
tertia cujus Ordinata BF aequalis eft fecundae areae 
A E B ad unitatem applicatae, & A G M C Curva 
quarta cujus Ordinata B G aequalis eft tertiae areae 
A F B ad unitatem applicatae , & A H N C Curva 
quinta cujus Ordinata BH aequalis eft quartae areae 
AGB ad unitatem applicatoe, & fie deinceps in 
infinitum. Et funto A, B, C, D, E, &c. Areae Cur- 
varum Ordinatas habentium, y, zy, z'y, z^y, z^'y, 
& Abfciffam communem z. 

Detur AbfcilTa quaevis AC=t, fitq; BC=t— z 
= x, & funto P, Q, R, S, T areae Curvarum Ordi- 
natas habentium x, xy, xxy, x'y, x^y & Abfciffam 
communem x. 

Terminenter autem hae areae omnes ad Abfciffam 
totam da tarn A C, nee non ad Ordinatam pofitione 
datam & infinite produ£!:am C I : & erit arearum 
fub initio pofitarum prima ADIC=A=P5 fecunda 
AEKC=tA-B=Q.Tertia AFLC-^-^^=f5±c ^,j^^ 

Quarta AG MC :^ 5 . 3^-3 Wc-d _,^^ q^j^^^^ 

A H N C rrtrr l4A>-4t:!B4-6ttC--4tD ^E ___ I ^ 

24 24 1 , 



CO- 



[ 207 J 



COROL. 

Unde fi Curvs3 quarum Ordinata- funt y, zy, 
z*y, z'y, &c. vel y, xy, x'y, x^y, &c. quadrari 
poffunt^ quadrabuntur etiam Curva^ ADIC^ AEKC, 
AFLC, AGMC, &c. & habebuntur Ordinatae BE, 
BF^ BG, BH areis Cur varum proportionales. 



Quantitatum fluentium fluxiones efle primas ^ 
fecundas, tertias, quartas , aliafq; diximus fupra. 
Hae tluxiones funt ut termini ferierum infinita= 
rum convergentium. Uc fi z" fit quantitas fluens & 
fluendo evadat z-l-o]", deinde refolvatur in feriem 
convergentem z^'-j-MOZ^-^-i-^ooz «-'-f- "^ - ^'^^ "^ ' Vzr^ 

\^ &c. terminus primus hujus feriei z" erit quan- 
titas ilia fiuens, fecundus «oz""' erit ejus increment 
tum primum feu differentia prima cui nafcenti pro- 
portionalis eft ejus fluxio prima ^ tertius —^ oz«'^ 
erit ejus incrementum fecundum feu differentia fe- 
cunda cui nafcenti proportionalis eft ejus fluxio 
fecunda, quartus "3-3wi-4- ^" qSzh-? erit ejus increment 
tum tertium feu differentia tertia cui nafcenti 
fluxio tertia proportionalis eft, & fie deinceps in 
infinitum. 



t T? - - 



Jbxponi 



[ 2o8 ] 

Exponi autem poffuiit hoefluxiones per Curvarurn 
Ordinatas BD, BE, BF, BG, BH, &c. Ut fi 
Ordinata BE (=^) fit quantitas fluens, erit 
ejus fluxio prima ut ordinata B D. Si B F (=M?^ 

fit quantitas fluens, erit ejus fluxio prima ut Or- 
dinata BE & fluxio lecunda ut Ordinata BD. Si 
BH ("=—2) fit quantitas fluens, erunt ejus fluxio- 
nes, prima, fecunda, tertia & quarta, ut Ordinata^ 
BG, BF, BE, BDreipeaive. 

Et hinc in aequationibus quae quantitates tantum 
duas incognitas involvunt, quarum una eft quan- 
titas uniformiter fluens & altera eft fluxio qugelibet 
quantitatis alterius fluentis , inveniri poteft fluens 
iila altera per quadraturam Curvarurn. Exponatur 
enim fluxio ejus per Ordinatam B D, & fi hoec fit 
fluxio prima, qua^atur area ADB=BExi, ii 
fluxio lecunda, quaeratur area AEB:=BFxi^ fi 
fluxio tertia, quaeratur area AFB^^BGx i, &c.= 
& area inventa erit exponens fluentis quaefit^. 

Sed & in aequationibus qu^ fluentem & ejus 
fluxionem primam fine altera fluente , vel duas 
qufdem fluentis fiuxiones, primam & fecundam, 
vel fecundam & tertiam, vel tertiam & quartam, 
&c, fine aiterutra fluente involvunt : inveniri pof- 
funt fluentes per quadraturam Curvarum. Sit 

tsquatio aav = av -U vv , exiftente v :== B E , 

v =BD, z=:==AB & Zr=i, & aequatio ilia com- 

plendo dimenfiones fluxionum, evadet aav == avz 

-|- vvz, feu ^fqr^ ~z. Jam fluat v uniformiter & 

fy 



[209] 

fit ejus fluxio v=i & erit £^=z, & quadrando 
Curvam cuius Ordinata eft ^^^ & Abfclffa v, ha- 
bebitur ttuens z. Adhaec fit aequatio aav=av^-vY 
exiftente v=BF, v=:BE, 'v=BD & z=AB & 
per relationem inter V & v feu BD & BE invenie- 
tur relatio inter A B & B E ut in exemplo fuperiore. 
Deinde per banc relationem invenietur relatio in- 
ter AB & BF quadrando Cur\ram AEB. 

^quationes quse tres incognitas quantitates invol- 
vunt aliquando reduci polTunt ad sequationes quae 
duas tantum involvunt, & in his cafibus fluentes 
invenientur ex fluxionibus ut fupra. Sit sequatio 
a — ^bx^=cxyMy -(-dy^^'yy. Ponatur y«y=v & erit 
a — bx^"cxV']-dvv. Ha^c sequatio quadrando Cur- 
vam cujus Abfciffa eft x & Ordinata v dat aream 
v^ & oequatio altera y"y=^v regrediendo ad fluentes 
dat 4-7*^^"^ =v. Uiide habetur fluens y . 

Quinetiam in irquationibus quae tres incognitas 
involvunt & ad aequationes quse duas tantum in- 
volvunt reduci non poffunt, fluentes quandoq; 
prodeunt per quadraturam Curvarum. Sit ^quatio 
a x'^+ b x^p = r e x^-' y ' -]- s e x^ y y'-' — f y y^^ exiftente 

♦ « 

X = I . Et pars pofterior r e x^'^ y ^ -'l- s e x^ y y ^"^ — f y y ^5 
regrediendo ad fluentes, fit exry' — ^JL.yM-r q^^^ 

proinde eft ut area Curvas cujus Abfciffa eft x & 
Ordinata ax"' i-bx')^ & inde datur fluens y. 

E e e Sit 



[2I0] 

Sit aquatio X X aJr + bx^P := JntL. Et fluens 1 

cujus fluxio eft X X ax^^i-bx*'^ erit rut area Curvag 
cujus Abfcifla eft x & Ordinata eft a x^^ .4- bx«l^. 
Item fluens cuius fluxio eft -ip^ erit ut area Curv^ ^ 

cuius Abfcifla eft y & Ordinata -^J^^ id eft 

(per Cafum i. Formae quartae Tab. I.) ut area 
^^fy%^y«r Pone ergo ""^Ve-^fy" aequalem areae 

Curvae cujus Abfcifla eft x & Ordinata ax^^^j^ bx^l^? 
& habebitur fluens y. 

Etnota quod fluens omnis quae exfluxione prim^ 
coUigitur augeri poteft vel minui quantitate quavis 
son fluente. (lux ex fluxione fecunda colligitur 
augeri poteft vel minui quantitate quavis cujus 
fluxio fecunda nulla eft. Quae ex fluxione tertia 
(^oUigitur augeri poteft vel minui quantitate quavis 
cujus fluxio tertia nulla eft. Et fie deinceps in in- 
finitum, 

Poftquam vero fluentes ex fluxlonibus coUedt^. 
font fi de veritate Conclufionis dubitatur, fluxio- 
nes fluentium inventarum viciflim colligend^ funt 
& cumfluxionibus fub initio propofitis comparandae. 
Nam fi prodeunt aequales Conclufio rede fe Ha- 

bet: 



[211 J 
bet: fin minus, corrigenda^ funt fluentes fie, ut 
earum fluxiones fluxionibus fub Initio propofitis 
aequentur. Nam & Fluens pro lubitu affumi po- 
teft & affumptio corrlgi ponendo fluxionem flu- 
entis alTumptae oequalem fluxioni propofitas, & ter- 
minos homologos inter fe comparando. 

Et his principiis via ad majora fternltur. 



F I N I 



ERR JT J. 
BOOK I. OfOptlch. 

PArt I. p. 3. 1.20. Tropertiesrohich, ib.p.5. 1.5. and that C, p. 6. I.9. DE^ p.2i. I.23. 
arj twoJ{ajs, p.27. 1.6. f;? t/^e M^irgmput Fig.14 ^ i^y.-p.-^oA.j.MNyl.g. M, p. 
44. 1.15. a/srvaspropofed, p.52. 1. 17. ^ i'-^i"?^ C/Vde, p.57. l.ult. emerging, t;).6o. 1.25.' 
£-o«toWTO/t/» tky p.64. 1.18. ^wrf i4t^> p.65. i.13. ^rrk, p.66. 1.3.>S'e»x/c/?T«/^r, p.67. 
1.25.Cew?e?-, 1.31. 4I /;?ck^, p.68. 1.8. to 16, I.9. or ^|, p.71.1.1. ^i/eff, p.72.1.13. 
/^&, 1.20. i'ew^. Part II. p.S6. 1.5. klopipede, p.89. I.9. wi^^e ^j/, p.93. 1.18. to 77^^ 
i.28,29, by the third Jxiom of the firft Pan of this Book, the Lawsy p. 105. l.'^.fee repre- 
fented, p. 144. 1. 24, i, j-^^, /„, f, A, f^g, ^. P- "S, "P- ^r X/^.i. if^.2. write 
-n. ., n....^ i_ j„j.Vo -r. Tor^ 1 To +/i the /ivinifl f^ i'^ 2, 1.6. bj the bright' 



p- 

BOOK. II. 

P.5. 1. i^.vicely t/;e,p. 7. 1.9.^? ^ detjote, I.28. tkw divers,-p. 10. 1. 24. 1000 w 1024, 
p.ii.Lii. oli^uitiesyj. p.17. 1.4^ Hf ^9, p. 25. 1. 11. i of^ p.31. 1. 12. wiore cor/i- 
pounded, p.55. [.-^.fi^esrefleB:, I.24. (?wi therefore their Colours arife, p.65. 1.5. cor/?w_/:. 
c/a- a?/, p.71. 1.17. give?t breadth, p.84. 1. 4. are to thofe, p. 96. 1. 24. Ohfervation of 
thU Part of this Booh, p.103. 1.17. wa/s to the thicHefs, p. 105. 1. 19. of this r?hite E^/jg, 
p. 1 07. 1.20. become equal to the thiM oj thofe. 

£mimeratio Line arum. 

•^.\\l,\.^Q. ditas fig;MsfiiiSy ^,\4\.\.2l.refpiciunt, p. 146. l.'j.funtJfymptoto, p, 
154. 1.13. cx-\-d dat Ordinatmy =5 , i.i4» q^u^ generatur. 

Ouadratura Cwvarum.. 
p.i68.1.24.re5.z^5,p.i76.1.ult. ^^ ^^^ fz.«,p.i83.1.i3.^,&,c,SJ(r. e,/;^,^^. fc>^ w» 

■^c, p. 18^. 1.4. i;z z&-i» P'lS^- l-H- zB±m p. 190. 1. 19- 'y^^ ^9-ri- F^. 
^. 192. 1. iS. a2,pH-2fj. p.193.1.11. aSy-l'bRr;*^' 



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